User Groups can be used to group a number of users in to logical groupings. The purpose of the group is to help administrate many users at the same time for example handle permission sets, user profiles etc. All operations done on a user group are actually performed directly on each user that belongs to the group at that moment. It is not applied to a user added to the group later. In the same way the effect is not removed if you remove the user from the user group. You can think of a User Group as an advanced selection of users.
Note: These User Groups should not be confused with Finance User Groups. These are defined in Business Roles/Accounting Rules.