Schrödinger's cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of an early interpretation of quantum mechanics when going from subatomic to macroscopic systems.
Schrödinger proposed his "cat" after debates with Albert Einstein over the Copenhagen interpretation, which Schrödinger defended, stating in essence that if a scenario existed where a cat could be so isolated from external interference (decoherence), the state of the cat can only be known as a superposition (combination) of possible rest states (eigenstates), because finding out (measuring the state) cannot be done without the observer interfering with the experiment — the measurement system (the observer) is entangled with the experiment.
The thought experiment serves to illustrate the strangeness of quantum mechanics and the mathematics necessary to describe quantum states.
The idea of a particle existing in a superposition of possible states, while a fact of quantum mechanics, is a concept that does not scale to large systems (like cats), which are not indeterminably probabilistic in nature.
Philosophically, these positions which emphasize either probability or determined outcomes are called (respectively) positivism and determinism.