First I had better start off with a disclaimer. Everything said in this thread needs to be taken with a fat table spoon of salt because this stuff is right on the edge of modern day theoretical physics, so we are likely to saying things that are somewhat wrong, or stated incompletely.
That is if anyone else post anything at all.
When particles meet with anti particles, they negate each other and transform into pure energy, meaning their complete masses are converted via E=mc^2 (which is otherwise essentially impossible).
So why are we here at all if when anti-matter and matter interact you get a fat explosion of energy? That is because there is a lot more matter in the universe then anti-matter. Simply put, the universe is not symmetric in the regard.
(NOTE: Some theorists argue that it is, but that there are regions of concentrated matter and anti-matter that are separated from each other for whatever reason.)
So if you like to think about particles moving forward in time and anti-particles moving backwards through time, then you could say that as a whole, the universe progresses forward through time due to the majority of matter vs. antimatter. This sort of makes sense, since we have defined ourselves to be moving forward through time.
If you really extend out the time logic though, there are some issues with it. One issue is the big bang. If at time = 0, there was all the energy in the universe compacted into a singularity which then went boom, spewing out the universe and all of the matter and anti-matter comprising it, then how can anti-matter be moving backward through time?
As in, it is violating causality. The bang, which marks the beginning of time, produced it, yet at time = dt, the anti-matter is moving back towards time = 0.
Hence, some theorists argue that the particles don't REALLY move backward through time, but rather they move backward through existence. No this doesn't make much sense to me either, and so I'll stop here for now.
A fun little thing to view is: http://youtube.com/watch?v=370fefE19S4
The first 4 minutes or so are unrelated (and I wonder who that kid is and where they dug him up from) but the rest is more interesting. http://youtube.com/watch?v=YiJJnHMSxWg&mode=related&search=
is the next part of this episode. Here they illustrate the absolutely beautiful experiment to first detect cosmic rays and then show a picture of a particle collision inside a detector and how matter and antimatter can be seen being created from energy. It is really neat.
In fact, the whole series in quite interesting and fun to watch, especially the black holes episodes.