A dominant, in color photography, is a color that came out stronger than it was supposed to, generally to the detriment of its complementary color (not to be confused with color shift).
Usually, when inspecting a color print, you can recognize cyan, magenta, yellow, green, blue and red dominants; recognizing the dominant gets you half way to getting a good color print.
Nearly everybody can tell if "the colors are off", but it is more difficult to guess at the dominant: a useful tool for determining which color is crushing the others is a set of viewing filters, that also helps in correcting the filterpack.