From Wikipedia:
To further illustrate, Schrödinger describes how one could, in principle, transpose the superposition of an atom to large-scale systems. He proposed a scenario with a cat in a sealed box, wherein the cat's life or death depended on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead (to the universe outside the box) until the box is opened. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, the paradox is a classic reductio ad absurdum.[2] The thought experiment illustrates quantum mechanics and the mathematics necessary to describe quantum states. Intended as a critique of just the Copenhagen interpretation (the prevailing orthodoxy in 1935), the Schrödinger cat thought experiment remains a typical touchstone for limited interpretations of quantum mechanics. Physicists often use the way each interpretation deals with Schrödinger's cat as a way of illustrating and comparing the particular features, strengths, and weaknesses of each interpretation.
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
