The online meaning of this scribbly horizontal line came to signify an
individual user's Web site on an ISP's server. The tilde stands for a path which leads to that person's Web site on the server, for example, http://www.best.com/~erinj - says that erinj is a best.com user and that her homepage is on best.com's server. If you look at the server logs you would see that erinj's Web site is really located on the path: www.best.com/www/users/erinj , therefore the tilde is used to bypass the /www/users directories to make the URL or "Web address" a shorter and easier to remember.
The tilde character is on the top line of a keyboard to the far left. It also can mean "around" or "approximately" as in "We've raised ~$10k so far."