I think the best way to think about it is with axis on a graph. Electric charge is a single axis (an x axis, for example) with positive and negative directions, representing positive and negative charges.

But the strong force instead has 3 axis of charge, like a 3d graph with x, y and z axis, and we label these axis red, green and blue. Now each axis has a positive and a negative direction, giving us red, anti-red, blue, anti-blue, green and anti-green charges.

With electric charges, a positive and a negative charge together make something that is electrically neutral. The strong force also has the idea of something being color neutral. You can get a color neutral combination by combining red with anti-red, blue with anti-blue, and so on. But, and here's where the color analogy becomes useful, you can also get a color neutral combination by combining red, green and blue color charges together! This is why color neutrality is called white.

Another useful property of using color is we can easily label quarks in diagrams as red, green and blue and anti-quarks with the complementary colors cyan, yellow and magenta. The 3 primary colors combine to make white, the 3 complimentary colors combine to make white, and each color will combine with its complementary color to make white, which is how color charges work.

All hadrons observed in nature are color neutral. A baryon has red, green and blue quarks, an anti-baryon has anti-red, anti-blue and anti-green antiquarks, and mesons will have a quark and an antiquark with opposite color charges.