The avatar is the small image that goes next to your name at the top left of each post. The signature area is at the bottom of each post and it can also have images and other graphics. The forum software can be configured to allow both and to limit the sizes of images/graphics used. I think it's a nice feature and I suspect that Len just hasn't had time to configure it yet. It can be different for specific user groups, so it's not just about turning it on or off.
It does take server space, but if the images are kept to a reasonable size (I would consider the small image in Dick's signature, at 32KB, too large a file size), the server the site is on now should be able to handle it nicely. In the end, though, it's up to Len.
PS: Dick, give my attachment a whirl. That's only 6KB and has a slightly smaller footprint too (only the height was changed).
I don't work here anymore.