When two things appear as opposites, they are contrasting. You might like the contrasting dark and light areas of a painting, with the clash of shades making it more interesting.
A clue to the meaning of contrasting is the prefix contra-, which means "against": when something is contrasting, it's working against something else. The contrasting colors of the fabric create an unexpected sense of movement, even though they should be working against each other. Two people with contrasting opinions, such as a liberal and a conservative, usually won't get along very well. But once in a while, contrasting world views can spark an exciting exchange.