Well, basically, the experiment was a mockery of the quantum theory.
The quantum theory says, in summary, that when things happen on an atomic level, it becomes reality when someone observes it-and until then, it sort of, "Isn't true." I butchered the explanation, but do you get it? You observe it and it's real. Until then, nothing's happened...kinda. It's hard to explain.
So Schrödinger proposed the following test: You take a cat and put it in a box. You then take a radioactive material, and arrange it so there's a fifty fifty percent chance that, in an hour, an atom will decay. Thus, it's quantum related. You have a geiger counter, and if the atom decays, the geiger counter will go off. This will, through a fairly simplistic mechanism, cause a device to spray the cat with poison.
According to the Quantum theory, the cat, when in the box for an hour, is simultaneously dead and pissed off at the humans/homicidal.