Yeah, the avatar goes alongside your PSN ID in your friends list or on any Sony-run PS3 forums. Changing it should be under Account Options.
But what's this about avatars walking around buying stuff? :huh:
PSN "Home" is a sims style social program attached with to the PSN for free, its technically in beta, for the past 3 years. Anyway, you can have a "avatar" and walk them around through various enviroments or "spaces" and interact with other players.
Here, check the links:
http://us.playstation.com/psn/playstation-home/
http://www.google.com/images?hl=en&sugexp=ldymls&xhr=t&q=playstation+home&cp=13&bav=on.2,or.r_gc.r_pw.&wrapid=tljp1299873496963014&um=1&ie=UTF-8&source=og&sa=N&tab=wi&biw=887&bih=572
The avatar you're talking about is simply a image associated with yout PSN tag. Home is a whole other boat...but it essentially breaks down to a giant mess of advertisemants trying to get you to buy virtual junk lol.