This end user SharePoint Tutorial shows how to delete a SharePoint group. This setting is a little bit hidden in the user interface.
A SharePoint group is in most cases the connection between an object that needs to be secured (e.g. document, site) and a set of permissions defining allowed or permitted actions which members of the group can do.
Groups are already known from Active Directory where you can put Active Directory users in security groups. This is done when an employee joins a company, gets promoted or leaves the company. SharePoint groups are defined during the planning of a new SharePoint portal and doesn't change that much. There are for example authors, readers and maybe some super users with more rights than authors and less rights than a site collection administrator.
A use case for deleting SharePoint groups may be the merging of different authors for different sites into a single SharePoint group instead of many different.
How to delete a SharePoint group
If you want to delete a SharePoint group go to site actions and open site permissions. In order to remove a group you need to click more and edit the group. Scroll to the bottom and delete the group.