Hmmm, parallel universes, this is a very complex topic, but I will try and describe it as clearly as I can.
At the moment, most scientists believe in 4 'levels' of different universes, or multiverses. Each level is a different scenario of how we think parallel Universes could arise and what they would be like. I'll just go through them one by one, but won't bother much with Level II and IV multiverses because they are nasty.
Level I
Note: In this, Universe applies to all the little universes (such as our own) put together.
Level I multiverses are based around the idea of 'Inflation'. Inflation is what we believe stopped all the matter created by the Big Bang recollapsing into itself moments after its spontaneous creation due to it own titanic gravity. I won't explain inflation here, that would take ages, just think of it as the heat of the Universe making it expand very quickly. Anyway, what many scientists think, is that inflation blew apart all the little 'grains' of early Universe that were starting to condense into smaller areas of space such as our own. This left all the little 'bubbles' of space stranded far away from each other, separated by billions of light years worth of void. I'll try to explain it in a diagram. We are area 'A' and there is another area 'B' which got separated from us in the moments after the big bang.
<-- area A, 13.7 billion light years radii -- > <- 50 billion light years gap - > <-- area B, 13.7 billion light years radii -- >
As the diagram above shows, both areas A and B can only see things in a sphere, radius 13.7 billion light years around themselves (Yes, I know Earth isn't the centre of our area of space (or universe), but because physics is broken, every point in our area of space/universe looks like the centre of it). But, due to inflation there is a gap 50 billion light years wide in between the two areas, which means neither area will encroach on the other, or be aware of the other's presence for another 50 billion years. Effectively, they can be thought of as different universes.
Seeing as matter can pop out of nowhere in a vicious way, we can effectively think of the number of these small, separate universes as being infinate. You might think this would lead to an infinate number of different universes, but, quantum mechanics tells us that there is only a finate number of ways of putting together all the atoms in our universe, an enormous number, yes, but not an infnate number. This means that somewhere, approximately 10^10^115 metres away, there is an exact copy of our Universe. We can then lead this on to say that anything you can think of the Universe being like, will exist. Which means that there could be a universe where life took an extra 1000 years to develop, but apart from that is exactly the same, so if you could travel there, you would essentially have gone 1000 years into the past.
Of couse, finding out which universe you want to go to, and how to get there may be impossible, but nevertheless, the chances of such a scenario as described above being reality, are pretty high.
Level II
Level II multiverses arn't worth talking about much. Essentially, a level II multiverse scenario is if the Universe (There's only one main universe for this unlike Level I) has multiple 'buds' of smaller universes, formed from minature Big Bangs, leading off it via wormholes. If you found a way of traveling through wormholes you could go to them, but physicists expect that in bud universes, there is a good chance of universal constants being different. For example, gravity could not exist, or magnetism could be strong enough to tear us apart, so you wouldn't want to go to them.
Level III
Our current idea of what Level III multiverses are and how they form was first thought up by the American scientist Hugh Everett III, he invented the 'Many Worlds Interpretation' of quantum mechanics which essentialy states that whenever a decision is made, a two or more new realities form, each accomodating for each possible outcome. This would lead to an incredibly large number of parallel Universes, seeing as even the slightest movement of an electron could be considered a decision.
The famous 'Schrodinger's Cat Box' thought experiment captures the essence of a Level III multiverse rather well. Whilst the box is closed, only 1 reality exists, the moment the box is opened it splits into 2 realities - one in which the cat is dead, the other in which the cat is alive. Of course, this is very simplified but it does explain the basics.
Level IV
Level IV Universes are aslo not worth talking about seeing as they are the least likely. Essentially the theory behind it is, that each mathematical function has a Universe which was created by it. In a way, Level IV and Level II multiverses are similar seeing as universal constants would be different and probably kill you if you tried to go there.
And that's all I'll write for now, I'm sorry if it sounded like a science lesson, but I hope you enjoyed it.