The movie is place in the future where parents get to choose their children's DNA. The main character however, his parents did not choose his DNA.
As he grows, he finds that he most wants a job as an astronomer. The only problem is that he is misjudged by the people who have chosen DNA and they think he is not worthy of the job. He decides to save up money working as a janitor at Gattaca (an astronomer job place) where he dreams to work.
One day, he meets a man who has all the right DNA to work in Gattaca but he hates it there. The man agrees to let our main character, Victor, act as him. Arrangements are made and Victor gets the job. Everything goes as planned until his boss is killed and the place goes out of their way to find the murderer. While at work, an eyelash of Victor's drops to the floor and the detectives find it to test whose it is. They find out it is his and set out to find who is disguised as another.
I will not tell more and give it away but, if you want to know more, see the movie.