The User Group Assignment is quite useful for when you need to assign a box to be displayed only on specific Joomla User Groups such as Registered users, Administrators and so on.
In the table below you can see which options are available to setup the User Group Assignment.
With this option you are presented with the entire tree of all your available Joomla User Groups.
You are able to select from one to all of them just by checking the checkbox to their left.
Obviously the most common use case for the User Group Assignment is when you want to show your box only to those who belong to the Registered Users, meaning the logged in users. Those of course include not only your lowest level users but the managerial users as well.
It's equally important to remember that users can belong to more than one user groups. This means that while you're using this Assignment and testing things out, don't be alarmed if you see an Administrator being displayed your box while you have selected the Manager role for example. He could be also assigned in the Manager User Group.