What has the Quantum Theory got to do with Parallel Universes? (A bit of an explanation included inside)

I just know it could as well be a dog!

Well the idea is that at every moment in time there are things that could go one way or another. Put simply, the way that Quantum Theory relates to Parallel Universes is that, at each of the junctures, both possibilities occur creating a parallel (but slightly different) universe. Because there are an infinite number of events there are an infinite number of universes and this increasing exponentially all the time.

There is a film called The One, it explains parallel universes really well, Red Dwalf also did a few episodes on parallel universes with Ace Rimmer but they didn't include much scientific information

What you are describing sound's like the work of Niels Bohr, he suggests that things don't happen unless witnessed. The work of Huggh Everett III has largely surpassed Bohr's. Want to understand Everett's Many Worlds theory in a way that doesn't cause your brain to leak out of your ear?

Watch this, it was on Monday night but knowing the BBC oh so well, it will be repeated dozens of times.
http://news.bbc.co.uk/1/hi/sci/tech/7113098.stm copy

It has a brilliant soundtrack provided by Hugh's son Mark or 'E' as he's known, which makes it even better.

This is Hugh's paper at Princetown if it makes sense to you:
http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html copy

This is a very good FAQ on the whole subject:

http://www.hedweb.com/manworld.htm copy

The theory of quantum mechanics is widely accepted because it works. It predicts what the outcome of many experiments will be and has enabled us to control nature in new and amazing ways. It has given us - for good or ill - cheap plastics, fast computers, atom bombs, designer drugs, lasers, cell phones...

But none one knows how to explain it in human terms, maybe because our common sense view of reality does not extend to the world of the very small. There are, however, many possible 'interpretations' of the theory. One of these calls for the existence of a vast number of parallel universes. One strange feature of quantum mechanics is that some events cannot be predicted for certain; all we can do is work of the probability of something happening. So, the Multiple Universe Interpretations suggests that in such a case, every possible outcome occurs – in a different universe.

I think what you have described there is a variation of Schrodingers cat thought experiment.
It is not so much that there are parallel universes with the cat existing dead and alive at the same time but what it tries to explain is that subatomic particles can exists in a a different number of states at the same time. and if the death or life of the cat depended on which state the particle was in then it would also be dead and alive until you actually opened the box and looked at it.
That is if you do not measure it or interfere with a particle it can exist simultaneously in many states. Its sort of the phenomenon behind what people are basing quantum computing and cryptography on.

Just a suggestion - Phillip Pullman's His Dark Materials books deal with this through story (and are brilliant) but there's a book by Mary and John Gibbins called The Science Behind His Dark Materials which explains quantum theory easily enough for me to follow. I thibnk it would help.