it's a movement in the arts (philosophy and writing, mainly.)
i ripped this off an existentialist website, and it seems to be pretty fitting.
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Existentialism attempts to describe our desire to make rational decisions despite existing in an irrational universe. Unfortunately, life might be without inherent meaning (existential atheists) or it might be without a meaning we can understand (existential theists). Either way, the human desires for logic and immortality are futile. We are forced to define our own meanings, knowing they might be temporary. In this existence, the individual defines everything.
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if anyone read/studied the real inspector hound, waiting for godot, or rosencrantz and guildenstern are dead, they're all existentiaist plays. the quest for meaning in a meaningless universe, morals, fate and choice, that sort of thing. i can't think of how this might apply to an artwork though. existentialism as a theme is pretty broad.