Schrödinger's cat is a theoretical experiment thought up by the physicist Erwin Schrödinger to demonstrate the logical absurdity of superpositioning of probabilistic quantum states.
His thought-experiment included a radioactive substance, a geiger counter, a hammer, and a flask of poisonous fumes, which would be contained inside a box with a live cat. The geiger counter would be hooked up to a device to release a hammer, breaking the flask, releasing the posionous fumes and killing the cat. Supposing quantum theory predicts that the radioactive substance has a 50% chance of emitting one decay particle every hour, after one hour there would be an equal chance of the cat being alive or dead. Now, quantum theory would predict that the cat is neither alive nor dead but something of a mixture. But when the box is opened to observe the results, this superpositioning of states will collape and the cat will either be alive or dead.
This paradox presents the problem of what causes the collapsing of the wave function. If it is the act of observing, then can the subjects own consciousness cause this collapse? This question was posed by Eugene Wigner, and still remains a bit a mystery. Most physicists treat quantum mechanics as a toolbox which can be used to accurately solve complex problems, but for which the nature of observation still remains unexplained. Numerous explanations for quantum measurement have been proposed, but none have gained prominent acceptance.
McEvoy, J.P. and Zarate, Oscar Quantum Theory for Beginners ISBN 18741666374
Schrodinger's Cat references on the web
The Interactive Schrodinger's Cat page has an expanded explaination of the situation as well as a button to simulate the experiment by providing a random outcome.
An online comic by the name of User Friendly featured a comic as a joke about Schrodinger's cat, explaining that Schrodinger's experiment is the only valid use of a blink tag.