Avatars are images which are shown next to a member's posts and in their profile, and can be added wherever else you desire. To upload an avatar, the member goes to their Options -> Edit Profile page. When they upload their desired picture it's automatically resized to the size you specify at Admin -> Settings -> Files.

At Admin Panel -> Settings -> Switches you have the option to turn avatars on or off. When on, individual members can select in their profile to not view them if they find it distracting or a waste of kilobytes.