It is important to note that no actual cats, real or superpositioned, were harmed during the creation of this wiseGEEK article. (Inside joke for physics majors).
Erwin Schrödinger was a contemporary of other eminent physicists such as Albert Einstein and Neils Bohr, although he was more interested in a relatively new field called quantum physics. Quantum physics in general went against much of what Einstein and Bohr considered to be scientific fact, which led to a number of high-level debates between Schrödinger and Einstein. One of those arguments contained a paradoxical thought experiment we now know as Schrödinger's Cat, although the cat was never more than theoretical.
One of the inherent problems with subatomic systems is the difficulty of human observation. One can assume that subatomic particles behave in a certain way, but introducing a microscope or a camera to observe them in action can negatively affect the natural behavior of the subatomic system. This would be the equivalent of a classroom of students changing their behavior once they discovered a documentary film camera crew in the room. The same thing happens when physicists try to observe very small objects.
"Schrödinger's Cat" is essentially an object lesson on the problems of relying on observation alone when dealing with subatomic systems. Schrödinger suggested an experiment in which a living cat would be placed in a cage on one side of a metal tube. Near the cat would be a vial containing poisonous gas and a trigger mechanism. A scientist would place a very small amount of a radioactive substance on the other end of the tube. This radioactive material would decay at a rate of one atom per hour, but the chances of that occurring are fifty-fifty. If an atom were indeed released, it would cause the vial of poisonous gas to break and the cat would die. No atomic decay would mean the cat lives.
Once this theoretical tube was sealed, no outside observation would be possible. No one would be able to check in on "Schrödinger's Cat" for an entire hour. After 60 minutes have elapsed, the question for the experimenter would be "Is Schrödinger's cat alive or dead?". Under Einstein's theories, the cat would either be dead or alive, with no middle ground. Only when the tube was opened and the status of the cat became observable could a definitive answer be found. Einstein would either see a dead or living cat, since God doesn't play dice with the universe.
Under Schrödinger's theory of quantum physics, however, the cat is actually in two different states at the same time. One version of the cat is dead, but another is still alive. This is the way subatomic systems would have to work as well, which sets up the paradox. A cat lives in a macroscopic system, in which objects either live or they don't. There is no middle ground, such as half a living cat. In quantum physics, however, the theoretical Schrödinger's cat could exist in various states, from completely alive to dead and all stages in-between. All of these states, known as superposition are possible outcomes from the experiment, although only one could be observed as true when the scientist examined the cat.
Schrödinger himself later expressed regret that he used a cat as the potential victim of a paradoxical thought experiment. His original point was to illustrate some of the problems of observing subatomic systems and drawing conclusions when the act of observation could skew the results. By taking the paradox out of the smaller subatomic world and moving it into the larger macroscopic world, Schrödinger did indeed prove his point to Einstein and others, but his theoretical object lesson would forever be known as "Schrödinger's Cat".