Here's how Wikipedia explains it:
A cat is placed in a sealed box. Attached to the box is an apparatus containing a radioactive nucleus and a canister of poison gas. The experiment is set up so that there is a 50% chance of the nucleus decaying in one hour. If the nucleus decays, it will emit a particle that triggers the apparatus, which opens the canister and kills the cat. According to quantum mechanics, the unobserved nucleus is described as a superposition (mixture) of "decayed nucleus" and "undecayed nucleus". However, when the box is opened the experimenter sees only a "decayed nucleus/dead cat" or an "undecayed nucleus/living cat."
The question is: when does the system stop existing as a mixture of states and become one or the other? The purpose of the experiment is to illustrate that quantum mechanics is incomplete without some rules to describe when the wavefunction collapses and the cat becomes dead or remains alive instead of a mixture of both.
In a nutshell: Put a cat inside of a sealed box, that can not be tampered with from the outside. Inside the box with the cat is a device that, after one hour, has a 50/50 chance of killing the cat. After the hour is up, the cat is either alive or dead, but according to certain rules quantum physics, until the cat is actually observed in one state or the other, it is, in fact, in both states simultaneously.
Which I think we can all agree is kind of ridiculous.
The point of Schrodinger's cat was to criticize certain points of quantum mechanics. Certain points which are, I can assure you, quite over my head. But I think Schrodinger's Cat beautifully illustrates a part of day to day life as well.
Every moment that is in front of you has potential. Until you seize the moment, make a choice, and take action, nothing is decided.
I can lay in bed for an hour wondering what to have for breakfast. And for that hour, every breakfast possibility is equally likely to come to reality. But the moment I grab the bowl and pour the cornflakes, the potentiality is gone and one particular course of action becomes fact, and then history.
Or, wait, here's a better analogy
It's like a game of russian roulette. One bullet in one chamber of a revolver. You spin the chamber, and put the gun to your head. In a sense, until you pull that trigger and find out for sure -- until you are actually able to observe the state of the chamber somehow -- it is simultaneously in both states at once. Kind of. In a sense.
Wait, forget that russian roulette thing. That's just gross.
But I think maybe you're getting the point by now anyway. So let's just drop the analogies.
As long as you're waiting to do something, as long as you're thinking about doing something, the potential exists for that thing to go in any of 1000 different directions. Once you do it, the potential is gone, and the cat is either alive or dead, no two ways about it.
That's the thing about life. Sometimes you make those choices, and everything just works out spectacularly, and you ask yourself how you could put that decision off for so goddamn long.
Other times, you wish you could have just held on to the potentiality, either because things didn't go the way you wanted, or were more complicated than you thought, or you just plain fucked up the choice somehow.
There's something sadly good about potentiality. There's something sadly good about just sitting within a situation where you have equal chances of success or failure.