Which users can award this hovering popup ?
It is part of the established user privilege.
When anyone is viewing your usercard on a question, an answer, or on the users list, they may hover over your avatar to produce an expanded usercard that contains extra information. This is also known as a hover card.
An expanded usercard is only available if there are at least 28 characters in the "About Me" section of your profile. When your profile is long enough to show an expanded usercard a drop shadow effect will be shown on your avatar.
How does it work ?