1. It's not a theory, it's a thought experiment or a paradox.
2. A cat is in a box with a geiger counter connected to a vat of poison in the presence of a radioactive source. If a decay event occurs, the geiger counter detects it, releases the poison and the cat dies. Otherwise, the cat remains alive.
3. The paradox comes in when considering the mathematical description of the system using the formalism of quantum mechanics, which by definition cannot be described in layman's terms. The point is that due to the inherent randomness of the atomic decay process, the wavefunction describing the system has terms representing the live cat and the dead cat, weighted by some probability. Until the cat is observed, its mathematical description will involve a superposition (linear sum) of terms describing the cat in a living and a dead state. However, once the cat is observed, the system will resolve into one state or the other - you obviously cannot observe a half-dead cat. So the question is: At what point, if any, does a quantum-mechanical system that is initially in a superposition of states collapse into a single observed state?
4. Schrodinger formulated this paradox in order to shake up the Copenhagen interpretation of quantum mechanics, which was the dominant interpretation at the time.
5. This whole scenario is based on a naive understanding of quantum mechanics, so don't lose too much sleep over it.