The Final Fantasy XIII series uses a lot of terms throughout its storyline, many of which are initially unfamiliar to the player. This page sheds some light on these terms.

Where available, I've taken definitions from the games' datalogs; I feel that the original source is the best definition available. However, where the datalog entries are lacking, or where there's some trivia I have to add, I've provided my own notes. These are in blue.

Because this site currently only covers FFXIII, this glossary also only covers that game. When I update the site to cover the other two games, I'll update the glossary as well. Spoilers are rampant in this section.

AMP Technology
Antimatter Manipulation Principle (AMP) form the foundation for a variety of technological wonders, enabling phenomena ranging from phase-space interference to the manipulation of gravitational force.
Humans ordinarily lack the means to wield magic, but through the use of manadrives - another product of the principle - it is possible to synthesize its effects.
The Sanctum has developed a vast arsenal of weaponry to defend against the constant threat of Pulse, and these living weapons are one of many fruits its research has borne.
Ordinary Cocoon wildlife transformed into efficient killing machinery through selective breeding, intense training, and physical augmentation, bioweapons retain all the raw power and feral fury of their natural counterparts while obeying the commands of their handlers with unwavering loyalty.
The brands that mark a l'Cie as one of the fal'Cie's chosen change gradually, passing through several different stages. When the "eye" at the center opens - the brand's final stage - the l'Cie become a Cie'th.
A brand's rate of progression depends partly on the difficulty of the l'Cie's Focus. It is also linked closely to the individual's mental state, with severe psychological trauma sometimes spurring rapid advancement. In the most extreme cases, severe fear and shock at being made a l'Cie has turned newly made l'Cie into Cie'th at the instant of their branding.
When a fal'Cie takes a human to be one of its l'Cie servants, that person is given a Focus to be completed. Should the l'Cie fail to fulfill this Focus before his or her brand advances to its final stage, that l'Cie becomes a Cie'th.
Mired in eternal sorrow and regret, and robbed of all free will, Cie'th are damned to wander the world, unliving and undying, until their corrupted flesh at last can move no more. For Cie'th, there is no salvation.
Cie'th Stone
L'Cie who fail their Foci become Cie'th, cursed to wander the wilds in a form of living death. Only after many years and much suffering do they extinguish the last of their strength and cease to roam. When this happens, the Cie'th's remains slowly fossilize, turning into what is known as a Cie'th Stone.
However, this transformation does not mark an end to the Cie'th's regret and sorrow at having failed. Even after having turned to stone the Cie'th cry out, imploring other l'Cie to fulfill the Focus they could not.
From her lofty seat, the world of Cocoon has long enjoyed tranquility. The interior of her spherical shell supports several sprawling cities and a population numbering in the tens of millions. Although a variety of dangerous beasts prowl the wilds, advanced technology and the protection of the world's fal'Cie keepers ensure residents a peaceful and prosperous existence. Travel to the lowerworld of Pulse is forbidden, but given their deep-seated cultural fears of the place, Cocoon citizens would not even think to venture beyond the paradise they know.
Crystal Stasis
For l'Cie, successful completion of a Focus holds the promise of eternal life in the peaceful slumber of crystal stasis - or so the legends say. Yet to spend an eternity as an immobile crystal is not so very different from death. The people of Cocoon consequently fear being marked as a l'Cie, equating the fal'Cie's brand with a death sentence.
Faced with only the choice between eternal damnation as a Cie'th and eternal imprisonment in crystal, it comes as little surprise that many l'Cie decry their fate.
These mystical entities reveal themselves before only a select few l'Cie. It is said that they are saviors, come to rescue helpless l'Cie who find themselves bound to a Focus against their will. If this is true, they offer a salvation few indeed would seek willingly: without exception, Eidolons attack the l'Cie whose presence they grace.
There have been no l'Cie in Cocoon for centuries, and as a result, no way of determining the truth behind tales of these beings. To the citizens of Cocoon, they remain the stuff of bedtime stories.
Obviously, the Eidolons in the game are the summons of the previous games, and serve the party members in battle.
from the pulse fal'cie entry:
Fal'Cie are an existence beyond human comprehension, possessed of incredible magic power. The ones responsible for Cocoon's construction are protectors of humanity, but there are others of their kind as well: the fal'Cie who dwell on Pulse and name themselves enemies of Cocoon.
Humans who encounter Pulse fal'Cie are cursed, being turned to l'Cie and ordered to destroy Cocoon. It is for this reason that most ordinary citizens support the Purge — anyone who may have come into contact with one of these fal'Cie represents a dire threat.
from the sanctum fal'cie entry:
The Sanctum fal'Cie are the unfathomable entities that constructed the floating shell of Cocoon in ages past, and even now watch over the world's human inhabitants. Each is assigned a specific task that supports the existence of Cocoon's grateful populace, such as generating energy or manufacturing food. The fal'Cie rarely intervene directly in the governing of society, leaving that responsibility to appointed human representatives. One theory states that, including the lower hierarchy, the total number of Sanctum fal'Cie exceeds eight million.
The Fifth Ark
This Gran Pulse structure lies deep below the capital city of Eden, its existence unknown to the members of the Sanctum.
According to legend, Arks are Gran Pulse armories that hold living weapons in stasis, in preparation for war with outside forces. These facilities also supposedly serve the function of awakening a l'Cie's latent powers.
Why this 'Fifth Ark' is on Cocoon, and whether there are other Arks hidden elsewhere, is uncertain.
Guardian Corps
The Guardian Corps is the branch of the Sanctum military responsible for maintaining peace and stability within Cocoon.
Within their assigned jurisdictions, the soldiers of the Guardian Corps fulfill the role of the police officers and protectors, working to eliminate all manner of criminal activity as well as rampaging wildlife. As a unit that works alongside the general population, it rarely employs heavy weaponry or cruiser-class ships. However, the Corps does retain squads of highly mobile shock troops.
from the pulse l'cie entry:
The beings known as fal'Cie possess the power to enthrall unwilling human instruments, compelling the victims to serve their will. These individuals, known as l'Cie, are marked with indelible brands. They gain the gift of magic, but also bear the burden of completing a task known as a Focus for their fal'Cie master.
Pulse l'Cie — tools of fal'Cie from the world below — are considered dangerous enemies of Cocoon's society. As there exists no means of removing the l'Cie brand and the curse thereby imposed, Pulse l'Cie are hunted relentlessly.
from the sanctum l'cie entry:
During the War of Transgression, a number of warriors were made into l'Cie to engage the forces of Pulse alongside the Sanctum fal'Cie. Since that time, there is no record of a Cocoon fal'Cie taking a human as a l'Cie.
It is possible that there have been unrecorded cases, but even if that is so, any and all accurate information about the nature of Sanctum l'Cie has been lost in the intervening years. Even Sanctum researchers have been able to achieve no more than speculation.
The paramilitary organization known as NORA is a group composed of like-minded youths, assembled by Snow and self-funded by the operation of a seaside café in Bodhum.
Functioning as a neighborhood watch of sorts, NORA members patrol the vicinity of Bodhum for trouble. Most often, "trouble" consists of encroachment by dangerous forms of wildlife.
NORA had never openly acted out against the Sanctum prior to the Purge, and because of this, the military had been content to turn a blind eye to the group's activities.
In the English localization, NORA is an acronym, standing for No Obligations, Rules, or Authority. In the original Japanese, it's a pun on the Japanese word noraneko, or stray cat, which is why there are so many cat jokes in FFXIII-2.

The Pompa Sancta
This festive nighttime dance parade depicts the events of the War of Transgression in a stylish and dazzling display of pageantry. Held in Nautilus, the production portrays Cocoon fal'Cie as Eidolons who combine their powers with those of flamboyant 'Sanctum l'Cie' in order to overthrow the villainous l'Cie of Pulse.
In the show's dramatic finale, a Pulse l'Cie transforms into an abomination reminiscent of Ragnarok before finally being slain by a righteous l'Cie from Cocoon.
The Sanctum military is composed of two main branches: the Guardian Corps, responsible for maintaining security in various jurisdictions throughout Cocoon, and PSICOM - Public Security and Intelligence Command.
PSICOM is an elite special operations unit charged with protecting Cocoon from Pulsian incursion. In contrast to the lightly armed Guardian Corps, PSICOM employs an array of advanced heavy weaponry and cruiser-class airships. As PSICOM bears responsibility for any and all threats of Pulse origin, it was PSICOM who conducted the Purge.
from the pulse entry:
Resting in Cocoon's shadow, the sprawling and enigmatic lowerworld of Pulse is home to a multitude of terrors. The land is commonly believed to be inhospitable to human life, and a strict ban on interworld travel forbids citizens of Cocoon from venturing there to challenge this hypothesis. Not even members of the Sanctum's upper echelon can claim to have seen the surface with their own eyes, but the attempted invasion by the world's savage armies several centuries ago is well documented. Widespread fear of a repeated assault persists among the populace even today, with colloquial references often likening the world to a manner of living hell.
from the gran pulse entry:
The savage world derives its name from that of the god Pulse. Its vast wilderness is populated by creatures ranging from the monstrous to the deadly, and its fal'Cie seem to have taken a decidedly less friendly approach toward human dealings than those of Cocoon, cultivating the land for settlement, but demonstrating little concern beyond that.
At one time in its history, Gran Pulse was home to a thriving civilization and many great cities. Now it is home to many great ruins, and people are nowhere to be seen.
Pulse Vestiges
from the lowerworld artifacts entry:
In the aftermath of the War of Transgression, regions near Cocoon's outer rim were left uninhabitable due to the severe trauma they had sustained. To undo this damage, the fal'Cie gathered materials from the surface of Pulse and rebuilt Cocoon's wounded landscape using them.
Bodhum was one city so affected, and like the others, it still bears lingering traces of post-war reconstruction in the form of leftover lowerworld artifacts. The Pulse Vestige that hid a dormant fal'Cie was one such artifact.
from the pulse vestiges entry:
The fal'Cie sculpted Cocoon in antiquity, using resources harvested from the world below. When Cocoon's shell was fractured in the war, they repaired it with raw materials again gathered from Pulse - buildings chief among them. Remnants of these structures, termed Vestiges, can still be found throughout Cocoon today. The centuries-old Vestige outside of Bodhum was believed to be nothing more than a harmless curiosity. The discovery of a Pulse fal'Cie inside its walls proved this false, however, leading to the detainment and subsequent Purging of countless citizens whose only crime was being in the wrong place at the wrong time.
The Purge
To the millions who call Cocoon home, the lowerworld of Pulse represents a constant source of fear. Suspected association with Pulse means stigmatization as an enemy of the state and all mankind - even for born and raised citizens of Cocoon.
The recent discovery of a fal'Cie from Pulse near the city of Bodhum cause widespread civil unrest. After placing the city's entire population under quarantine due to the possibility of contamination, the Sanctum then announced its intent to forcibly relocate the affected to Pulse in an emergency measure dubbed by authorities as the Purge.
Lightning, Snow, and the others saw a phantom vision of this beast upon their branding as l'Cie. In the dream, they witnessed the creature besieging Cocoon's capital of Eden, but whether this was a glimpse of past events or a vision of things to come was unclear. What is clear is that Ragnarok is inextricably linked to their Focus. The nature of that Focus, and what must be done to fulfill it, remains to be seen.
A vague entry to keep from spoiling the player. Ragnarok is the beast Fang became many years ago, and was her and Vanille's original focus as Pulse l'Cie. At the end of the game, she and Vanille turn into Ragnarok together in order to save Cocoon rather than destroy it.
Cocoon's central government, the Sanctum, holds supreme executive, legislative and judicial power. It also maintains directive authority over the military.
Despite the fact that Cocoon was built by the fal'Cie, and not by humans, fal'Cie opt to participate only superficially in governmental affairs, leaving Cocoon's administration entirely at the discretion of the human Sanctum and its Primarch, Galenth Dysley.
You know, aside from the fact that the Primarch is a fal'Cie.
The Undying
The Undying are fearsome Cie'th who, cursing their former fal'Cie masters for forsaking them at the end of their forced servitude, refuse to surrender their connection to this world.
Whereas normal Cie'th eventually cease their wanderings and turn to stone, the Undying rage on, fueled by a jealous hatred of all living things. Retaining the defiant strength of will they knew in life, they act on instinct, doling out death and destruction to all that dare cross their path.
War of Transgression
Several hundred years ago, the armies of Pulse attempted to invade Cocoon in a conflict known today as the War of Transgression. The Sanctum's fal'Cie were able to repel the lowerworld forces before they breached Cocoon's interior, but not before they managed to seriously damage areas lying near the world's outer rim.
Details surrounding the clash remain shrouded in mystery, but the government's swift and decisive response to this violent Pulsian transgression minimized casualties and greatly boosted public faith in both the Sanctum and their fal'Cie.
Accounts vary on how long ago exactly the war was, but based on Fang and Vanille's physical ages, it's about 600 years before the start of the game.
Wide-Area Response Brigade
The Wide-area Response Brigade is a Guardian Corps unit commanded by Brigadier General Cid Raines. The brigade is famous for its unofficial name, the 'Cavalry'. A mobile unit without a designated jurisdiction, the Cavalry patrols the uninhabited expanses between cities, ready to respond to emergency situations at a moment's notice. For this purpose, the brigade commands a cruiser-class airship - the sole exception in the Guardian Corps.