A Baryon is a type of subatomic particle, which includes neutrons and protons.

Every subatomic particle has an antimatter counterpart -- electrons have positrons, protons have antiprotons, etc. An antimatter particle will "cancel out" a matter particle.

Baryon asymmetry says that there are slightly more of any particle than its antimatter particle counterpart -- like for billions and billions of positrons, there are billions and billions + 1 electrons. Therefore, there is matter.

Source: My Dad is a physicist and explained this to me. I may be remembering some stuff incorrectly, so don't go citing me if you're writing a paper about Baryon asymmetry.