Erwin Schrodinger helped to pioneer the field of quantum mechanics during the 1920's, when it was still in its proverbial infancy. One of the unique ideas attributed to Schrodinger is his equation concerning the evolution of quantum states within physical systems. (Schrodinger's famous equation) Schrodinger's theories would later become some of the basic building blocks of Quantum Mechanics. At the time Schrodinger probably didn't realize that he would be remembered for a strange little thought experiment he worked out in 1935, (Schrodinger's Cat Paradox.) In which a cat is placed into a sealed box for a given length of time. Inside the box is a device containing a radioactive isotope and a trigger mechanism. If the isotope decays spontaneously (as they sometimes do) then the trigger is tripped and allows a hammer to drop onto a glass vial of poison. Once the poison has been spilled the box will flood with toxic fumes, instantly killing the cat, as seen in the above diagram. His big question: At a given time, without opening or looking into the box, what is the state of the cat? The cat is part of a physical system (essentially a closed system) which is either a lethal or a non-lethal environment depending on the quantum state of the isotope-trigger mechanism and the corresponding poison-release mechanism at that exact time.
The common sense answer is that the cat can only be in one of three states, dead or alive or somewhere in the process of dying (easy enough.) Quantum Mechanics, (notably Schrodinger's equation) says that the answer isn't that simple. As with much of QM, things tend to go from weird to weirder to weirdest - this is no exception. After a given length of time has progressed, the cat is said to be both dead and alive at the same time! It is then the act of opening the box and observing the cat that brings about the observable state of the cat. This same act takes place whenever we peer into the subatomic world of the electron, or view the "Color Phi Phenomenon" or the famous "Double Slit Experiment." We are experiencing the strange yet ordinary world of quantum states within physical systems, as they evolve over time.
It is important to remember that this experiment did not take into consideration Bryce Seligman DeWitt - Hugh Everett's MWI of QM. Instead this experiment sought to describe the events of the system in the terms of a more classical view of QM. MWI was initially rejected by mainstream physics in favor of more classical Newtonian physics and its related theories. It is important to note that the laws of "classical" or "Newtonian physics" do not hold up when applied to systems within the quantum scale. Strangely enough, objects and systems that are this small have their own set of unique laws which govern behavior of particles and systems. It is for this reason that QM emerged in the first place, to explain these new troublesome questions and paradoxes. So what does the MWI (Many Worlds Interpretation) of QM have to say about the Schrodinger's Cat Experiment? MWI would say that 1.) there are more than just the one cat and system involved, 2.) the cats and systems exist within an infinite system (we can call that the "omniverse,") 3.) the cats and their systems exist in an infinite number of states within that infinite super-system - at least one experimental cat per universe or "world-line" exists in one definite state (dead, alive, dying, zombie, mutant, slightly sick, happy, sleepy, confused, enlightened or non-existent.) The previous list is meant to be slightly humorous, but you get the picture right? Sometimes the cat changes color, sometimes it was never there in the first place, sometimes the experimenter becomes the cat, sometimes it vanishes into a puff of smoke and sometimes that little hammer doesn't break the glass vial of poison. Why so many crazy options to choose from? Because this group of cats exists in universes where all those things are possible, even one where the cat mutates, grows to the size of a lion and eats the observer before they can even know what has hit them. Universes where these "novel" effects frequently take place might simply have a different set of physical laws governing the discreet action of particles or Newtonian physics may be completely re-written. It is likely that we in this universe share some degree of these strange effects with all others. It is also likely that the laws which govern our own universe exist (at least in some fashion) within others. This is a thought experiment (largely because a real experiment would be difficult, and probably toxic to cats) but even if it were a "real" experiment, we could expect to see these kinds of results to occur across the infinite omniverse we live in. I'm not usually a betting man, but the universe I live in is only slightly random, with fairly predictable laws (at least on the Newtonian scale.) I don't often witness Tabby cats growing into lions and eating people, but I am not willing to throw out the possibility that somewhere out there it does happen. Because I do not witness it does not make it any less possible. After all, stranger things happen all around us everyday!
The sooner you begin to view the universe around you as a strange and sometimes random environment, the easier it becomes to learn about the very odd world of Quantum Physics and its Many Worlds Interpretation. The sooner you learn about MWI and QM, the sooner you become ready for the dawn of the Quantum Age.
(portion below from Wikipedia free online encyclopedia) of Erwin Schrodinger's Equation http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#General_quantum_system
General quantum system
For a general quantum system: