The Avatar Shop is an exclusive feature for Kongregate's version of Enigmata: Genu's Revenge. You can enter it by entering a red portal that occasionally appears in the game. There, you'll find all of the characters you've met, and you can click one of the buttons to automatically change your Kongregate account's avatar to that of the chosen character. Of course, the Avatar Shop only works if you're playing the game using a Kongregate account, not as a guest!