Avatars are small icons representing you. Your avatar is shown on your user profile, on any and all comments you make (if the commenting functionality is enabled on the wiki) as well as on the user board messages you've sent.
You can upload an avatar by going to Special:UploadAvatar on a wiki with the SocialProfile extension installed , either directly by clicking on the link or going there via your user profile and clicking on the "Upload avatar" link. Your avatar image must be a jpeg, png, or gif and must be less than 100kb in size. Select a picture fitting the criteria and then press the "Upload" button to have the image uploaded to the wiki's server.