Joel Barish (Carrey) and Clementine Kruczynski (Winslet) meet for what they think is the first time on a Long Island Rail Road train from Montauk to Rockville Centre. They are unaccountably drawn to each other despite radically different personalities.
As it turns out, they were once lovers, but after two years their relationship was in a decline. Clementine decided to break up with Joel and hired a New York firm called Lacuna, Inc., to erase all memories of him. Joel was disconsolate upon finding out what she had done and decided to undergo the procedure himself. However, while unconscious and having his memories of her erased, he rebelled, realizing he wanted to hang on to his memories of her after all. Much of the film takes place in Joel's mind as he tries to figure out how to preserve some memory of his love for Clementine. We watch their love and courtship go in reverse, as the memories are slowly erased while they both try their best to resist the procedure and hide. Courtesy of http://en.wikipedia.org/wiki/ Eternal_Sunshine_of_the_Spotless_Mind