Dominant means to be in control. In a wolf pack, one male wolf fights the others, wins, and is considered the dominant, or alpha male. The other wolves in the pack do what he tells them.
Dominant derives from the Latin dominus which means "lord or master." If you grew up with a Latin mass, you will recognize this as one of many words for God. If you're dominant, it means you treat others as if you're their master. You can also use dominant to describe something frequent or common. For example, when cell phones first came out, their dominant use was for making calls. Now cells phone do so much more, some people hardly make calls on them at all.