In short, Final Fantasy XIII is stunning with only a couple letdowns.
In Final Fantasy XIII, humans live on a paradise world called Cocoon, which is a (mostly) encased-in-a-shell planet hovering over a larger world called Pulse. Cocoon was created by godlike machine-beings called the Fal'cie who watch over the humans and take care of their every need while protecting them from the "dangers" of the lower-world. However, things begin to fall apart and it is revealed that the Fal'cie are not quite so benevolent as once thought.
This story is done so incredibly well. The plot constantly surprises the player and never bores. The story of an dystopian society being rebelled against is one that is becoming common in today's culture, and people never tire of it in the least.
Furthermore, the characters are all wonderfully crafted together. Each of them has an unique, believable, and admirable personality (especially in comparison to the previous characters of Final Fantasy XII), and they all make the player want more. Also, unlike previous games where the plot centers on one or two characters, with the rest being backups and not used much, the plot of FF13 centers on the entire group as a whole, with all of them playing great roles in the story.
Onto the graphics, this is probably the first obvious thing that blows everyone's mind away. The world(s) of Final Fantasy XIII is simply amazing. The scenery is beautifully put together, and even the bleaker, darker settings are detailed to a level like never before. And this isn't only just for cutscenes. The regular gameplay visuals almost just as beautiful. Think back to the cutscenes of Final Fantasy X, and those graphics qualities are what FF13 has on a regular basis.
To add, the music is also great. Leona Lewis' "My Hands" makes a great theme to the game, and the rest of the soundtrack doesn't disappoint either. Particularly, the battle theme is one that gets the player so immersed into the game like no Final Fantasy has done before.
Next, the battles. FF13 doesn't have random encounters, but rather, you see the enemies on the map and can encounter or avoid them as you please, much like Final Fantasy XII. However, like the rest of the series, encountering them takes you to battle them on a different screen.
This game's active time battle system is similar to Final Fantasy XII's, in that the player chooses an action, and then the bar fills up, executing the action after it's full enough. Unlike FF12, the ATB is divided into sectional bars from three to six, and different actions require a certain number of bars. For instance, the basic attack needs only one bar while "Fira" needs to. With this system, the player can chain actions together (for instance, using the six bars to execute two Fira spells and two attacks) or fill up the bar partway and then halt the charge to perform the attacks in the middle.
This system is one of the most innovative and involved one's of the entire series. It keeps the player constantly on his or her toes, as the battles require so much more strategical and tactical planning than ever before. Another thing is that the battles are fast. Really fast. Not that the battles ends quickly, but that the speed that the characters and foes move and act are incredible. It will take some time to get used to, but the battles are the most immersive of all the Final Fantasy games.
During the battles, the player will only control one character, with the other acting automatically based on what class-role they are currently assigned. You can assign and reassign roles to them in and out of battle, such as Ravager, Commando, and Medic. (Basically, Black Mage, Warrior, and White Mage.) There are more, but you'll find out about those. Anyway, the AI for the automatic control of the other two characters is actually quite good, with the characters acting just as well (and sometimes even better than) the player him or herself would. The only downside to the one-character control is that it only takes the lead character to die to lose the battle, but it doesn't amount to too much problem.
One other great thing about battles is the camera. While other combat games may have an obscuring view of their battles with awkward angles and obstacles, the FF13 camera constantly swerves and pans to honestly give the player the best view of the battle as possible. No joke.
There are no character levels in this game. Instead, each character has something called a "Crystarium", which is similar to FFX's Sphere Grid. Enemies award character with "CP", which can be used to advance to new nodes on the Crystarium to gain stat-boosts and abilities. This system actually gets quite entertaining, and players may occasionally find themselves referring to the Crystarium after every battle, eager to see what new enhancements they can achieve.
The exploration of FF13 is a little on the weak side, however. Think back to the linearity of Final Fantasy X. It's just like that, or maybe even a little more. Right from the start, the game sends the player through one straight-line dungeon after the next (occasionally having a few side paths to some treasure). In that sense, no one will ever lose their way in this game, but sometimes it becomes boring. The only exception to this is an area on the planet Pulse, which is reminiscent of FFX's "Calm Lands" in that it is a huge, vast plain with loads of enemies and a fair number of things to do.
Another thing that may make players sorry is that there is no town exploration at all. As simply as above, one dungeon after the next. (Well, some of the dungeons ARE cities, but there's no city-interaction.)
As for sidequests, FF13 has what are called "Cie'th Stone Missions", which are basically the same as the "Hunt" from FF12. When the player encounters one of these Cie'th Stones (you'll learn what exactly these are when you play the game) they are given a mark (or enemy) to track down and kill. However, these quests, while are fun for the sake of going out to slaughter things, aren't all that immersive. For the most part, they go along the lines of "head north and kill please", rather than making any real quest out of them.
Overall, FF13 is a fantastic game. With amazingly immersive battles, plotline, characters, music, and scenery, the issue of linearity can be easily overlooked. Any fan of the Final Fantasy series should play this game with no exception, as they will all have a blast right up to the end. (Was it mentioned that this game's final boss is likely one of the most challenging of the entire series?) So all in all, enjoy!