How does color charge work?

There are three color charges and three corresponding anticolor (complementary color) charges. Each quark has one of the three color charges and each antiquark has one of the three anticolor charges. Just as a mix of red, green, and blue light yields white light, in a baryon a combination of "red," "green," and "blue" color charges is color neutral, and in an antibaryon "antired," "antigreen," and "antiblue" is also color neutral. Mesons are color neutral because they carry combinations such as "red" and "antired."

Because gluon-emission and -absorption always changes color, and -in addition - color is a conserved quantity - gluons can be thought of as carrying a color and an anticolor charge. Since there are nine possible color-anticolor combinations we might expect nine different gluon charges, but the mathematics works out such that there are only eight combinations. Unfortunately, there is no intuitive explanation for this result.

Important Disclaimer:

"Color charge" has nothing to do with the visible colors, it is just a convenient naming convention for a mathematical system physicists developed to explain their observations about quarks in hadrons.