Back in the Olden Days (long before Linus or Linux), you logged in to a Unix system with a "teletype" (tty).
Flash forward to today (or at least anytime in the last 10-15 years ;-)), and you're likely to log on to a *nix system (Linux, Unix, OpenBSD, Mac, etc) with X Windows.
The ":0" specifies which "display" of a particular host's "X Server" you're logged into.
Here's a bit more info:
http://stein.cshl.org/genome_informa.../xwindows.html
'Hope that helps .. PSM