In a very limited nutshell, existentialism is the study of human existence and the doctrine that our actions have consequences and certain things are not predestined to happen; that we really do have control over our own lives. This appears to tie in with the line in the song that stands out most, "Sing like you think no one's listening." In essence, lead singer John Nolan is saying that in high school (i.e. prom night) we care far too much about the reactions of others to our actions and that true happiness lies not in what a group thinks of you but what one special person thinks of you. It's sort of a carpe diem type of thing.
James - Woodstock, GA