A personal avatar (pavatar) is an image hosted on your own site.
[it] is then used by websites to display whenever referring to content provided by YOU, the user. An example would be if you made a comment or a site posting where an avatar is required.
Contrary to services such as those of gravatar.com (which might be having long-term problems), you are freed from dependencies to foreign servers; as long as your server is reacheable, your personal avatar will be served to sites which ask for it. The Pavatar site consicely explains how to create a personal avatar (an 80x80 image in png, jpg or gif format), how to publish it, and how to check it. It shouldn't take longer than a minute or two to set up.