It's about people with various psychic powers. People called "movers" have telekinesis. People called "pushers" can implant ideas or memories into other people's heads. People called "watchers" can see the future (though the future is always changing). And there are various other types, but those are the most important three in the movie. It actually starts 10 years before the main timeframe of the movie, when a guy named Nick (a mover) was a kid, and his father (also a mover) was killed by a team led by a pusher named Carver (Djimon Hounsou). After World War II, there was an agency started called the Division (or I guess there are "Divisions" around the world), for which Carver works. In the present, Nick (Chris Evans) is living in Hong Kong, basically just trying to stay under the Division's radar. He's not very good at "moving," but he does get better, as the film progresses. Anyway, some Division "sniffers" find him; they're looking for a girl who had recently escaped from a lab, along with a syringe of a drug that could enhance psychic abilities, though the girl was the first test subject to survive the injection. Nick, however, hasn't seen her, and the sniffers leave.
Immediately after they're gone, a 13-year-old girl named Cassie (Dakota Fanning) shows up. She's a watcher, and wants Nick's help to find the same girl the sniffers were looking for. He doesn't want to help her at first, but for various reasons (including part of the advice his father had given him ten years earlier), he does end up helping her. The girl they're looking for is supposed to be able to lead them to a case, which the Division is also looking for. But also there's a Chinese group who are looking for the case. I'm not sure if they were a rival division, or a gang, or what, but they're a family, including a couple of "bleeders," who have sonic screams that make you bleed from your ears, and potentially kill you. The family also included a watcher, who becomes a nemesis to Cassie. (Cassie calls her "Pop Girl," because she's always sucking a lollipop.) But the main antagonist in the film is once again Carver, who is always accompanied by a very powerful mover named Victor (who, naturally, becomes a nemesis to Nick, though he's not as interesting a nemesis as Pop Girl).
Anyway, Nick and Cassie are aided by a few other psychics with various powers, and eventually they find the escaped girl, a pusher named Kira (Camilla Belle), who is apparently an old girlfriend of Nick's. The movie is complicated by various twists, and it's not really clear what to believe, because anything a character does believe could be false memories implanted by a pusher. And of course there are "wipers," who can erase memories. And most of the time, Cassie's visions of the future involve her and her allies dying. But of course, the future can be changed. So... I dunno, it's just a complicated movie, but I definitely found it interesting and cool. I like the ideas that are presented here, though in spite of being sort of mind-bending, it's not as clever as it could be. Mostly it's just an action movie with a sci-fi twist. But it definitely could have been a lot worse, so it's a shame it wasn't well-received, critically or financially. A sequel would have been nice.