Antimatter is like matter on opposite day: it has the same properties as the stuff that makes up planets, stars and galaxies, but one vital piece is different—its charge. The universe supposedly started off with equal parts matter and antimatter, but somehow, matter won out. Most of both substances annihilated each other shortly after the big bang, and left a small surplus of matter remaining.
Answer
This was answered well in the comments but I'll write it up as a proper answer. There are two main questions here:
- Why is there an asymmetry between matter and antimatter?
- given that there's an asymmetry, why did matter win out?
The second question is answered rather easily. The Big Bang produced more of one of the two types and everything, from galaxies to human beings, ended up made of this. Since we're made of that type, it is no surprise we ended up calling that one matter and the exotic type antimatter. This is not an intrinsic distinction, though: there is nothing in the lab that distinguishes antimatter from matter.
The real question, of course, is why there is more of one type to begin with. Indeed, as far as we can tell, all the pair production mechanisms that would have turned energy into mass just after the Big Bang ought to create equal amounts of matter and antimatter. Nevertheless, we observe more of the former and less of the latter.
This question is, alas, completely unresolved. We simply do not know. This 'baryon asymmetry problem' is currently an open and active research field, though no one really knows what the solution might look like. If we do find out, though, be sure that you will hear about it in the news, and that there will be a Nobel prize or two for the people that resolve it.
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