Downloadable Content, or DLC, is bonus content released for a game and often available for a small fee. Quite a lot of it was released for FFXIII-2, and you can learn about it all right here.
If you haven’t played FFXIII-2 yet, your first stop after buying the game should be to buy the bundle of its DLC, which gives you the vast majority of its bonus content in one place. It’s much more cost-effective than buying it all separately, and only leaves out a couple of items.
You might be wondering: do I need to get the DLC at all to enjoy the game? Unfortunately, this is the part where I tell you: yes, you do. FFXIII-2’s ending is inconclusive at best, and its actual ending takes place in the “Requiem of a Goddess” DLC. (Square was roundly criticized for this move.) If the only thing you care about is the story, then that’s the one you’re going to want to pick up.
The other story-relevant DLC is the Sazh “Heads or Tails?” DLC. In all honesty, it’s not a very good DLC, in either story or gameplay; it’s tedious and adds very little to the game. (This is a real shame, considering how great of a character Sazh was in the first game.) In theory, the Snow DLC also has a story, but you’d be hard-pressed to find one considering how nonsensical it is and how little relevance it has to the rest of the game.
There are costumes. There are a lot of costumes. If you like dressing up your playable characters — or you just don’t like Noel and Serah’s default outfits — then that’s a fine reason to go pick up the bundle, which includes most of their alternate outfits. This is the main draw of the pack; you can get them all at once instead of buying them separately. There are a couple of outfits not included in the pack, largely for licensing reasons; these include the Mass Effect and Assassin’s Creed outfits.
Because FFXIII-2's cutscenes are rendered in-engine, Serah and Noel wear whatever costume you've chosen for them in both battles and in cutscenes. The only time they won't be wearing the outfits you picked are in the pre-rendered full motion videos. You can see art of these outfits on in the gallery.
There’s also an outfit pack for Mog, because why not.
The bundle includes some weapon DLCs, but they’re not really worth it. You’ll get the best weapons in the game by playing it. Same goes for the ones not included in the pack.
Yes. There are a lot of them. Gilgamaesh makes a return (of course), as do Ultros and Typhon, who like jumping into everything these days. Omega from FFV is back. Even PuPu the alien from FFVIII shows up.
Somewhat inexplicably, you can fight Jihl Nabaat from the first game. There’s also a fight with Lightning and Lt. Amodar. Don’t look at me, I don’t really get it either. I just want the monster crystals.
The Final Fantasy Wiki has a full breakdown of all the DLC in the game, if you want more specific details about pricing and availability.