The tilde (~) is a grapheme which has several uses. The name of the character comes from Spanish, from the Latin titulus meaning a title or superscription, and is pronounced "TILL-duh" (IPA /'tɪldə/) in English or "TEEL-day" /tilde/ in Spanish. It was originally written over a letter as a diacritic (see below), but has since acquired a number of other uses as a character in its own right
Every command-line-loving geek will tell you that ~ stands for home directory, and cd ~ will take you to your home directory. (cd ~username will take you to someone else’s, except on Mac OS X, where it will take you to their Public file sharing directory.)
In fact, Jukka has written a lengthy treatise on why the tilde should not be used in URLs, a treatise which, I feel obliged to point out, contains a tilde in its URL.