Schroedinger's Cat, Putatively
Schroedinger said that you could demonstrate the concept of quantum superposition by thinking of a cat sealed in a steel box. (Don't worry, this is just a thought experiment.) There is a flask full of poison near the cat. If the flask shatters, the poison is released and the cat dies. If the flask does not shatter, the cat lives. But, Schroedinger asks, is there a state in which the cat is both alive and dead? Quantum mechanics would indicate that the states of alive-ness and dead-ness of the cat would coexist simultaneously. While a state of alive-ness slowly gives way to a state of dead-ness, there's a liminal time in between when both states are true.
Quantum mechanics is based on the theory that complex numbers called amplitudes can be assigned to events, the way we think of probabilities. While many have accepted this postulation, some have objected to the assumptions it leads to. This theory helps us predict the movements and behaviors of subatomic particles, but as we (and Einstein, famously) might object, life isn't like that; you're alive or you're dead. Right?