Lucy (Scarlett Johansson) is an American student living in Taiwan who gets tricked by her boyfriend into working as a mule. In order to transport the controlled substances, a packet of CPH4 (a valuable synthetic substance) is sewn into her abdomen. While she's in captivity, however, one of the men attacks her and ruptures the bag, releasing a large amount of CPH4 into her system. Under the power of the substance, Lucy is able to use more of her brain function, while most humans (according to a debunked, but fun, myth that the film takes for its premise) can only use around 10%. With this increased function, she gains powers of telepathy, telekinesis, and mental time travel.
Lucy contacts a scientist, Samuel Norman (Morgan Freeman), who may be able to save her from herself. She meets Norman and his colleague, promising to share everything she now knows, since her new purpose in life is the spread of knowledge.
Near the end of the film, Norman injects Lucy with more CPH4, and she dissolves into a black substance that spreads over the technology in the room, becoming a sort of supercomputer. She can now travel all the way back to the beginning of the universe, where she witnesses the Big Bang. Her consciousness melds with the world around her and we're told that she is now everywhere, having finally harnessed the full power of her brain.
This disintegration scene takes Lucy's fun, pulpy premise a step too far, into the realm of self-parody. The movie should have ended with Lucy's declaration that sharing knowledge is the most important thing in life.