I’ve been messing around on Yahoo! Answers recently. Someone asked the question “Why do some physicists think parallel worlds might exist?” I spent far too long on my answer (especially since the fun parts of quantum physics won’t be on my upcoming exams!) but am fairly pleased with it, and it took me back a bit to when I was studying such things. Answer reposted below:
That’s what is known as the “many-worlds interpretation” and is one of the ways scientists try and think about the baffling world of quantum mechanics.
The classic experiment and the best way to explain is the double-slit experiment. Imagine you have a plate with two narrow slits cut in it. You have a light on one side, and a screen on the other. When the light shines through one of the slits, it produces a diffraction (spreading) pattern. When it shines through both slits, there are two diffraction patterns which interfere with each other, producing a different interference pattern. This is typical for waves, and you can show a similar effect with ripples on water.
Now it is also known that light occurs in indivisible “packets” called photons. If you decrease the intensity of your light source you can get it to emit only one photon at a time. But you still get the interference pattern on the screen! Why is this weird? Because if you only sent one photon at once, what is it interfering with? The quantum answer is that it interferes with *itself*!
Somehow the single photon must have passed through *both* slits. There are a few ways to think about this. One basically says that it is impossible to know which slit the photon went through, and therefore it went through both. Unfortunately this basically means that the photon no longer has a position you can pin down, which is a bit weird. This is just like Schrödinger’s cat being in a box where you can’t tell if it’s alive or dead, so you say it is both at once. 
So as an alternative to that weirdness, some scientists  thought up an explanation just as weird, if not more so – the many-worlds interpretation. In this version, the photon remains localised (i.e. it has a defined position). But the universe splits! In one universe the photon goes through the left slit, and in another it goes through the right one. We only see what happens in one universe, so we think photons stay localised. And then somehow on the other side, the two universes interfere with each other to give the pattern. This is like saying Schrödinger’s cat is alive in one universe, and dead in another.
Hope this helps, and apologies for the length, it’s pretty complicated to explain and I got a bit carried away! There’s more info about the many-worlds interpretation here: http://www.hedweb.com/manworld.htm
“…those who are not shocked when they first come across quantum theory cannot possibly have understood it.” – Niels Bohr
 Schrödinger didn’t actually believe in his cat, it was just an example to show how weird quantum mechanics is
 Fun fact, the guy who proposed this first was the father of Mark Everett from the band Eels.