Mismatched things don't go together — they're too unsuitable or different from each other. Your mismatched socks, one with purple stars and the other with yellow stripes, are a perfect example.
Mismatched clothing might actually work for you, if wearing a velvet gown with ratty sneakers is a deliberate part of your personal style. But mismatched people usually don't fit together so well. If you're a vegetarian night owl and your friend is a burger-loving early bird, you'll make a mismatched pair on a cross-country road trip! Mismatched is from mis-, "badly," and the Old English mæcca, "companion."