The one girl a guy will always have a thing for, and will always do anything for. The girl a guy will never forget, even if there was nothing between them. The girl who is more, to the extent where, a guy will never be with this girl and is aware of the reality and so, realizes it will never be.
Steve- Why do you keep calling her?
Tom- I can't help it, she's my white elephant.
Steve- It's never gonna happen.
Tom- Yeah, I know, but not for lack of trying.