Moderators manage forums:
They decide, whether to close, move or even delete a thread.
They can edit text within messages, too.
 

Moderator

See above.

Super-Moderator

Super-moderators have the same capabilites as moderators have.
Additionally, they can create forums or change their options.
In contrast to moderators, their influence is not restricted to a forum, but covers a whole category.
They can instate moderators within their reach.
They can ban users.

Administrator

Administrators have the same capabilites as super-moderators have.
Additionally, they can create categories or change their options.
Their influence covers the whole board.
They can instate super-moderators.
They can give quota to users.
They can give additional titles to users.
They can delete users.

Webmaster

The Webmaster has the same capabilities as the administrators have.
This user is created during setup: The admin-account, being created during setup has Webmaster-permissions.
The Webmaster can instate administrators.

User lists are good for allowing a range of users specific rights.
Forums may be restricted in write- or even read-access to a certain user list.
Furthermore, it might be of use to create a user list for giving the same quota to a group of users, for giving quota can be done per user list as well as per user.
A user can be on any number of user lists.