Someone will be along shortly who can explain it much better than I, so I won’t try. I just want to point out that if you stop to think about it, you’ll quickly realize that we really don’t understand the electric positive/negative charges either. They don’t seem weird because we’re so used to them, but trying to explain exactly what a charge IS is all but impossible.
Smeghead has it right. The strength of the electromagnetic force depends on a quantity called “electric charge” which can be positive or negative and has to be an integer multiple of one third the charge of the electron. The strength of the “color” or “chromodynamic” force between two quarks depends on their color charges. Chromodynamics is much more complicated then electromagnetism and it just happens that there are three kinds of charge, which can also be in positive or negative. In electromagnetism, the particle that carries the force (the photon) has no charge. In chromodynamics, the analogous particle, the “gluon” also comes in three different colors, which makes things much more complicated.
Physicists understand these things at a deeper level as consequences of beautiful mathematical symmetries. These symmetries have been discovered, but no one knows why nature has them.