An avatar is a graphical image that represents a user. Either one can be a logo or a picture.
Your initials appear in your avatar if there is no picture.
Typically, you click you avatar to get access to things.
Your avatar appears in various places. Examples:
Assign Sections dialog box
Next to sections that have been assigned
In the Desktop app, the Getting Started page and Connection Mode page.
In the Work view, in Discussions.