Something variegated has many different colors, as in the trees of autumn or the feathers of a peacock. Whenever you see "vari" at the beginning of a word, you know that the idea of difference or change is involved.
Using vari is a good way to start thinking about this word. It's the same root as in various, variable, varied, and variety. All these words mean something similar: lots of different versions of something. The scales of a fish can appear quite variegated from one angle and then strangely uniform from another. A tiger's variegated coat helps it stay hidden.