Signatures are user defined messages that get attached to all their posts.
Most signatures you will encounter in this forums consist purely of text (thank god).
If you want an image in your signature you will have to acquire a toriprime, which costs you, as far as I know, ten USD a year.
Avatars are images you can upload to your profile. They get displayed right under your name whenever you submit a post.
If you want to use a bigger image or want it to be animated (gif) you will have to acquire toriprime.
You can edit your avatar and signature in your UserCP which you can access by clicking on “UserCP” in the upper left corner on the forums.