An Avatar is basically a profile picture. Avatars can be used on person-profiles. They can also be added to Events, Services and Groups. Each of these items has a default image, but including your own goes a long way in branding and recognizing one item from another.
Avatars are used as the visual representation of an item. They are shown on list views, in the portal, accessible through the API, used in our Event Kiosk and show up most places the title or name is used.
If you have access to the item, you can change the avatar. For example, if you've been given access to Groups, you can change the picture used for your group.