What you take out of this game really depends on what you expect from it. If you're looking for a freeplay sandbox, turn around and walk away. If you're looking for excellent character development, pull up a chair and settle down for the ride.
The world of Cocoon is a self-sustaining sphere suspended above the terrifying wilds of Pulse, and the Sanctum keeps Cocoon running smoothly. When a creature from Pulse is discovered in a resort town of Cocoon, the Sanctum tries to pacify the panicked populace by instituting the Purge: a forcible relocation of everyone who was anywhere in the vicinity of the tainted piece of Pulse.
The story begins in medias res, on a train of deportees, as a woman—codename Lightning—is preparing to break free. Being your primary protagonist, it's no surprise that she manages to do so. Most of the other characters are quickly introduced, the first chapter ricocheting between different perspectives to establish—or establish the question of—motives. Sazh is a good-natured everyman, and he serves as the player's voice in questioning the situation and actions of the others. Snow is rebelling against the government, a bit clueless about how to do it, and more than anything wants to rescue his fiancée. Hope is a terrified kid caught up in the midst of a rebellion, and Vanille is an overly cheerful enigma. The plot slowly unfolds over the course of thirteen chapters, each twist leaving your party more confused than before about the best course of action, not the least of which is the question initially asked: should they try to save the people of Cocoon, who hate and fear them for what has happened to them?
The battle system is a hybrid of FFXII's AI and the ATB used in almost all previous FFs, with a couple of major differences. Magic no longer consumes MP, and your characters are completely healed at the end of every battle. Characters assume different roles, which can be changed mid-battle by use of the Paradigm system, but cannot access abilities outside the designated role. If, for example, you have someone attacking in a Commando role, they would not be able to heal other party members unless you changed them to a Medic role. Similarly, someone in a Medic role is unable to attack.
On the plus side, buffs and debuffs are useful and worth casting, and the AI is reasonably good, if a little confused on priorities at the endgame. On the downside, you can't change lead character during battle, cannot control any character but your lead character, and cannot access any special abilities other than your lead character's. As every character has a unique summon and at least one unique ability, that makes on-the-fly changes impossible, but, since party death just means you can opt to retry the battle rather than forcing you to reload a previous save, it's not a horrible hindrance, just an annoyance.
Is Final Fantasy XIII the best game ever? No. Is it the best FF ever made? Probably not. Is it fun to play, beautiful to look at, well-acted, and generally a good experience for what it is? Definitely.