The user avatar (the icon besides your username) is taken from the independent site http://www.gravatar.com/ by converting the given email address on the user profile and turning it into an MD5 hash. A hash from the same input (here the email address) is always identical but it is not possible to calculate the original input from it. In other words: for a fixed email address you will always get the same avatar, but people won't be able to get your email address by looking at the avatar or its URL.
You can register at gravatar.com with any email address and upload any icon you wish. If this is not done, gravatar.com will automatically produce a random avatar from the email hash, like:
Now if no email address is given in the user profile your avatar might change frequently. This has happened to two users I know of which got a new avatar daily which is quite annoying in my opinion. The main reason for the avatars is to give a visual recognizable representation of that user. A frequently changed avatar (either automatically/accidentally changed because of an empty email address or manually by the user) undermines this and should be avoided.
Therefore if you belong to the users which don't want to give away their email address then please insert some random but constant address just to have a constant avatar. Please make sure that it is clear that the email address is just a placeholder, e.g.
firstname.lastname@example.org, but please keep it unique otherwise you will have the same avatar like someone else.