If you spend all day admiring yourself in reflective surfaces — mirrors, pools of water, the backs of spoons — people may think you are conceited or vain.
If, to your horror, you have searched everywhere for a reflective surface but can't find one, you have made a fruitless or vain search for a mirror. Vain is from Latin vanus "empty," and in English it originally meant "lacking value or effect, futile"; we still say "a vain attempt" using that sense, and the phrase "in vain" means "without success." Normally, though, vain means "conceited, too proud of oneself." Carly Simon's line "You're so vain, you probably think this song is about you" is an excellent illustration of this use.