*nods* I use ICQ all the time, because all my friends went to college in a different city. It's a cheap way to communicate compared to the telephone.
Depending on your circle of friends, satguru, you may be more familiar with AOL Instant Messenger (AIM) or MSN Messenger, which do the same thing as ICQ. I believe ICQ was the first of the bunch, but don't quote me on that. It is more likely just the one I HEARD OF first.
ICQ keeps track of its clients by issuing them each an individual number. You have a username as well, that you can change any time you want, but your ICQ number stays the same. The website you were at wanted you to give your ICQ number, so if other people at the site (I take it it was a social site?) who use ICQ wanted to contact you that way, they could.
ICQ doesn't stand for anything, really. But when you say it, it sounds kind of like "I seek you" which is kind of cute when you think about it.
btw, ICQ kicks AIM and MSN's butts!