An avatar is a small picture that kinda "represents" a user. It appears with their post and can generally be any picture of their choosing.
Go here for an example of avatars on another board I frequent. Just click on any one of the topics. The avatar is the picture appearing under another poster's name.
I agree avatars would be nice, but I prefer my GreekChat working and fairly ad free. If that's the only trade off I have to make, I'm not complaining.
And no offense, but sig pictures drive me crazy. I can hardly find the post for all the garbage.