Nobody seems to know about these...
An avatar is the image below your name. A signature is whatever you want, and is below posts. I think you should have these because it makes your profile more interesting, and rather than having to read the poster's name you can just look at their avatar. It also makes a lot of fun. For example, Nick's avatar is this:
But as soon as I saw it, I decided to make this:
Avatars and signatures can be changed through the profile, and signatures can be a lot of things. Most people just have an image that links to their site or something, though.