Manual:$wgGroupPermissions

Details
$wgGroupPermissions is a two-dimensional array indexed by usergroup and available permissions. The value can be either TRUE to grant the permission or FALSE if it should not be granted.

Those permissions, which are granted with $wgGroupPermissions are always cumulative: If a user is member of different groups, then the user will get a right if it is granted to at least one of these groups even if it is not granted to his other groups. In other words, If one of the user's groups has a right, then it is not possible to take the right away using $wgGroupPermissions. Instead use $wgRevokePermissions to revoke permissions.

Example
This gives all registered users the ability to edit pages.

Custom user groups
You can also define your own user groups; user group names can be no longer than 16 characters. The groups, which have been defined either in DefaultSettings.php or in LocalSettings.php, can be assigned to users through the wiki Special:Userrights interface.

Example
This creates a group called "Trustworthy". Users of that group have the same permissions as users from the group "user". However, they will be able to delete and protect pages, to patrol edits and to directly purge cached pages.

For in-depth documentation, see Manual:User rights.

Default values
Default values vary from version to version. You may find the one which apply to your mediawiki setup in DefaultSettings.php. For more info visit Manual:User rights.

Use by extensions
Some extensions, such as RenameUser or CheckUser, add new rights which can be configured and assigned in the same manner.