If something is complementary, then it somehow completes or enhances the qualities of something else. If your beautiful voice is completely complementary to your brother's song writing skills, you should form a family band!
You’ve probably heard of “complementary colors,” colors that are opposite in hue on the color wheel but actually go well together. When combined, they make a harmonious palette. People’s personalities can also be complementary, as can certain food pairings. But be careful not to confuse this adjective with the closely spelled complimentary, which means “supplied free of charge.”