The Time Traveler's Wife explores the way in which we experience memory, and how those memories can then affect our present lives. When Clare meets Henry in the present, she struggles with the fact that the memories she cherishes with him from times when she met him growing up mean nothing to him, since he was an older version when they spent time together. Not seeing in him the man she remembers suddenly makes Henry a stranger to her.
Memory also keeps the characters from overcoming pain and from moving on with their life. Henry keeps time traveling back to his mother's death, so he never quite gets past it. His father can't move on with his life, because he clings to the memory of his wife, and becomes lost in the grief of that. And after Henry's death, Clare acknowledges that it's her memory of him that keeps causing her pain.