color charge
Electric charge comes in one flavor with two signs, plus and minus, and opposite signs attract. The strong force needs something richer, so quarks carry a second, more elaborate kind of charge that physicists whimsically named color. It has absolutely nothing to do with the colors you see — it is just a memorable label for a property that comes in three varieties, playfully called red, green, and blue.
Here is the trick the naming captures. Just as red, green, and blue light combine to make white, a quark of each of the three colors can combine into a colorless, or "white," bundle — and that is exactly what a proton or neutron is: three quarks, one of each color, adding up to no net color. A quark can also pair with an antiquark carrying the matching anticolor to cancel out, which is what a meson is. Nature seems to insist that everything we can actually isolate be colorless overall; lone colored objects are forbidden.
Color is the charge of the strong force in the same way electric charge is the charge of electromagnetism. Particles with color feel the strong force; particles without it (like electrons) do not. The mathematics behind the three colors is a symmetry called SU(3), and building a force theory on it gives quantum chromodynamics — literally "color" (chromo) dynamics. The whole rich behavior of the strong force, including why quarks can never be pulled apart, flows from this three-way color charge.
A proton is "white": one red, one green, one blue quark. A meson is "white" too: a colored quark plus an antiquark of the matching anticolor (say red + anti-red).
Only colorless combinations exist as free particles — three colors that sum to white, or a color and its anticolor.
"Color" is purely a name. A red quark is not red; you could rename the three charges 1, 2, 3 with no loss. The visible-light analogy is a memory aid, not physics — do not take it literally.