Mirror's Edge is a unique and wonderful experience. There are some rough edges, but it's a beautiful and memorable game.
The closest gameplay comparison I can make is Portal. If you enjoyed the challenges in Portal 2, you will likely enjoy Mirror's Edge, too. The puzzles of both these games are about figuring out how to master a complex open 3D arena through trial and error, and the sense of fulfillment when you figure out the solutions in both games is similar.
Mirror's Edge is set in a beautiful near-future city, with abstract gleaming white towers and stunning vistas. Outside, you engage in parkour-style running, navigating high ledges and leaping from tower to tower, in a fluid manner. It’s similar to the more familiar Assassin's Creed games, but faster. Indoor sequences are more puzzley, usually about getting from Point A to Point B efficiently. The free running is exhilarating, both outdoors and indoors. Missing a jump by a faction of an inch and falling to your death will make your fingers tingle as you catch your breath! And there was a memorable close encounter with a subway train that made me jump out of my seat from the adrenaline surge.
Unfortunately, Mirror's Edge also features awkward combat sequences. The early training missions teach complicated combo moves for executing martial arts maneuvers. For example: blocking a punch while taking a weapon off an enemy. Honestly, these moves were way too complicated for me to execute confidently, but I quickly learned one easy combo that served me well in every situation: the slide-tackle. Turns out that if you take people out at the knees, everything else goes pretty smoothly!
These combat events are generally unwelcome in an otherwise excellent game. Disabling a cop as you round a corner, then dash away? That's fun. Disabling a cop, taking his weapon, and then having a shootout with his partners for 5 minutes, moving from cover to cover? This does not match the overall theme of the game, and it's a distraction. Fortunately, these combat events are few and far between, and not difficult enough to frustrate you, or dissuade you from completing the game. Think of them as a different kind of puzzle.
Last word: The trailer that Steam offers in the Store page is a poor choice. It features the cartoony animation from some of the between-levels cutscenes. The actual gameplay is more like this trailer:http://www.youtube.com/watch?v=2N1TJP1cxmo
Definitely consider Mirror's Edge; it's fine entertainment.