Question

What does a tilde symbol (~) usually mean at the beginning of a section of a web address?

Answer 1

It often denotes a certain user's webspace. For example, university.edu/~jsmith would be user "jsmith"'s personal webspace. Universities often give each professor a space like this to host his or her notes and other things for their students.

Answer 2

It comes from the unix notation of "~/" referring to your own home folder.

Answer 3

^ Also that. In Linux/OS X and other Unix-based OS's, ~ is equal to the entire path to your user folder.
I suppose you could say ~jsmith means the path to jsmith's user folder.