I will try to explain it as simple as possible and to the best of my knowledge. Anyway, it means that the very very small world or the quantum world doesn't work like our real macroscopic world. It is not deterministic meaning you can not predict the exact outcome of an event. In strict sense, the quantum world behaves probabilistically or statistically. Let's take for example an example of a simple coin flip. When you flip a coin, you know that there is a 50% chance that it will land either heads or tails. Since we have an equal probability, the result is very much random.
When early pre-modern physicists wanted to describe the very very small or the world of atoms, they wanted to know how electrons behaved, where the are exactly located, how they orbited around the nucleus,etc.... They restricted their calculations to their deterministic world of Classical physics as laid down by Isaac Newton. We all know or maybe some of us that this failed miserably. Going back to Schrödinger, he radically changed the way we view the atom or matter all iin general. Instead of knowing exactly, where the electron is, what we see is actually the statisticcs or probability of where the electron in an atom will most likely be (which is mostly everywhere). It is really confusing for people new to QM. It took me 2 eyars to completely grasp the idea.
Ok, going back to the coin flip, Schrödinger's cat is exactly like the coin flip. Schrödinger just really picked a random example as well. He couldn't have picked a more interesting situation. haha You have probably heard the story again and again. A cat in a box. Is it dead or alive? According to QM, it can be alive, dead or both until you open the box. It may seem like it doesn't make sense but that's how it is. And it has extremely meaningful and amazing consequences to modern physics and our universe. Our universe is not deterministic. We can only know the statistics/probability. We can never know how an event(experiment,etc..) would end up but we can, however, calculated the different possible outcomes and its corresponding probabilities.
Take for example, this die!
http://averweij.web.cern.ch/averweij/nepal/nepal_09.JPG It's not equiprobabilistic like the regular die which has 1/6 probability for each number. Now, it seems like 4 sides are more favored that the other two. (With lots of geometry and trigonometry, you can calculated this exactly.) If you take data from throwing this die several times, you will find that your result is simple statistics. In a nutshell, this is what quantum physics is all about. Not knowing what the exact outcome but knowing what to expect most of the time. Anyway, that's it. That's what I know. hehe Sorry for the long explanation. I hope I've shed some light into this topic. hehe