Rei is not a person. Not exactly. Biologically she is half human, half angel. She was cloned from Lillith, and her form was created from Yui's dna (Shinji's mother).
Rei II (the one who is seen throughout most of the series) fell in love with Shinji. After she died, her memory was scarred. Only slowly did her memory return to her. By the movies, she knew what to do. Go to Shinji.
