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Lead singer Adam Duritz wrote this song about denial. It's about when you're in a relationship with someone and you keep denying it's anything but a fling, then you wise up and realize that all along while you were denying it, you were growing closer together.
Anna is a girl from Australia that Duritz met on vacation in Greece in 1989. Apparently they still talk and she is a fan of the song. (thanks, Beth - Charleston, SC, for above 2)