Avatars are usually protagonist Blocksters (or, rarely, balls or other objects) which just about every world contains, usually always being controlled by the player via Mover, buttons, vehicle, dragging, or tapping tagged items, usually to defeat enemies or run obstacle courses. Blocksters themselves can be made to run and jump, and many different action blocks can be equipped and attached, such as lasers, thrusters, and even flight yokes.
Avatars can be created and objects added in a player's profile picture, usually to represent oneself in-game, either physically, or as a representation of one's wanted appearance. Profile Avatars are a great way to show off your Blockster look and some of your creations or a nice scene. They are probably most handy as being a quick way to access one's worlds and profile, by tapping the player's Profile Avatar directly from a world's description.