A flare is a sudden burst of light. The flare of a lit match in the dark night is strangely beautiful.
The flare of a flame in the dark is sudden and bright, and the flare of an idea or emotion is similarly intense. Parts of clothing that grow wider, like the "bells" on your bell-bottoms — and are also called flares. The verb flare also means to burn brightly or suddenly erupt, like a skin rash that flares up in hot weather or your friend's temper that flares when people tease her about her favorite team losing the big game.