Your avatar is the little picture next to your name in the upper right when a game is finished. If you click on it, then click Profile, then click on Change Profile Image under the picture. You’ll see a bunch of pictures you can select. Some of them that are under the Humans tab can be “bought” with coins.
Hope this helps.

I don’t know what the Levels mean.

Thank you, Crazy! I care less about buying pics for my profile. I thought the coins were for something good. LOL