Privacy and anonymity concern

[petit534]

I was recently on a forum where the bantering started to get a little heated. It was one of those "hate" places where I should not have been but kept going back like a moth to the flame. When I read the posts, I just felt like I needed to say something in defense of the people they were bashing. Eventually, a mod I guess, started addressing me by my real name and making references to other websites that I had frequented. This caused a chill...how much do they know and HOW do they know it??? When I asked how they got this information, they not only didn't answer but banned me from the site and the forum. I have since been able to access the site but still banned from the forum...even when I try to log in with a different email address and name.
I don't really care to participate in that forum again but just curious about how all of this works. Someone told me about the "IP". When you sign up for a forum, can they trace your IP and get this private information? Is it even legal for them to disclose your personal information on the forum?
Thank you so much for your help?