This is something I once had to write for a report to the dean, explaining (part of) what I do. The dean at that time was a history professor.
Particle Theory: Peter Arnold
By momentarily glancing up from this piece of paper, you can easily perform a simple experiment in cosmology: just notice that the room and everything in it is not exploding. If you happen to be an aficionado of Star Trek, you will immediately deduce that there is no significant amount of anti-matter in the room (since spaceships always blow up if their "anti-matter containment fields" fail). Anti-matter has the property that it can annihilate normal matter, producing energy. This annihilation is a quintessential example of Einstein's famous E = m c2, which says that mass m (in this case, a bit of matter and a bit of anti-matter) can convert into energy E (in this case, an explosion in the room).
A basic observation about our universe, then, is that it doesn't contain very much anti-matter compared to matter.* There's a certain puzzling asymmetry about that fact. Anti-matter, with the exception of some very rare processes that don't have much to do with everyday life, obeys the same rules that matter does: that is, if our bodies and the earth and everything on it and the sun were all made out of anti-matter instead of matter, we wouldn't notice much difference. It's only when matter and anti-matter come into contact that the effects are spectacularly noticeable. So why did the universe favor one cousin (matter) over another (anti-matter)?
The peculiarity of this asymmetry becomes more pronounced if one extrapolates back in time to moments after the Big Bang, when the universe was an incredibly hot, exploding fireball. As mentioned before, anti-matter can combine with matter to annihilate into energy. As far as has ever been seen in any experiment, this annihilation always occurs in pairs: that is, one bit of matter always annihilates exactly one bit of anti-matter, no more and no less. Similarly, it is possible to work Einstein in the opposite direction: a bit of matter can spontaneously appear from pure energy, but such creation is always accompanied by an exactly corresponding bit of anti-matter. Since matter and anti-matter always seem to appear or disappear in pairs, the difference between the total amount of matter and the total amount of anti-matter never changes -- at least as far as we know experimentally. Instants after the Big Bang explosion, there was lots of energy in the universe. As a result, lots of anti-matter was also present at that time, because energy is interchangeable with pairs of matter and anti-matter. The difference between the amounts of matter and anti-matter was still the same as today, and so there was more matter than anti-matter, but the total amounts of both were larger. At that time, energy and matter/anti-matter were constantly being converted back and forth. When the universe later cooled, and there was not enough energy to keep making matter and anti-matter, the bits of anti-matter eventually paired up with bits of matter and disappeared, leaving only the unmatched bits of matter behind (and no anti-matter) to make up the stars, the planets, and us.
Now here's the peculiar part. If one uses our current understanding of physics and cosmology to calculate the relative amounts of matter and anti-matter back near the beginning of the universe, one finds that there were roughly one billion and one (1,000,000,001) bits of matter for every one billion (1,000,000,000) bits of anti-matter. The state of matter in the universe today, and so our very existence, depended on the equality between matter and anti-matter being violated by one part in a billion. So why did the universe start with such a very small but essential asymmetry?
If it's really the case that matter and anti-matter always appear and disappear in pairs, then physics can give no satisfactory explanation. The difference between the amounts of matter and anti-matter today would then be whatever it was as the beginning of time: it's simply an initial condition on the universe -- an input to our theories of nature rather than an output. However, it turns out that there is a theoretical prediction that the forces of nature, as we currently understand them, can sometimes produce a bit of matter without an accompanying bit of anti-matter (or visa versa). The theory also predicts that this unusual phenomenon only occurs at the extremely high temperatures prevalent in the first billionth of a second after the universe exploded into existence. And because of these phenomena, the asymmetry of matter at time one billionth of a second can be different from, and indeed independent of, the initial asymmetry at time zero. The final amount of the matter left in the universe ends up a prediction (output) of the theory rather than an initial condition (input). Our understanding can be tested by comparing the predicted (actually, postdicted) amount of matter today with what is actually observed. However, turning the current qualitative understanding of the theory into a firm quantitative result requires much more work, as well as some further information from particle experiments over the next decade or two. The theoretical work on this problem has been one of Peter Arnold's main areas of interest.
* The alert reader may wonder about this assertion. The lack of anti-matter in the room doesn't mean there might not be far-away stars or galaxies made of anti-matter, so that there's a lot of anti-matter in the universe after all. Indirect observation can show that nearby galaxies are certainly not made of anti-matter. The puzzle would then become why matter and anti-matter are separated on cosmically immense scales.