What members are allowed to see and do
From Online Manual
There are a number of actions that members can be allowed to do and links that they can be given permission to on a forum. Most of these actions and links are handled by setting permissions the membergroups which members belong to, while a few of these settings are applied to individual members, regardless of which membergroups to which they belong.
What members can do on boards -- Board Permission Profiles
In SMF 2.0.x, a board permission profile is usually referred to as a permission profile. It is used by an administrator to control what different membergroups (and, therefore, the members in these groups) can see and do. Each board permission profile is a list, for every membergroup on the forum, of the actions that each membergroup which has that board permission profile can take, for example, start topics, reply to topics, modify own posts, or delete own replies.
Creating permission profiles allows administrators to pre-set permissions profiles which can then be applied to individual boards. Each profile allows the permissions to be set by membergroup. That profile can then be applied to one (or more) individual boards. When a profile (other than "default") is applied to a board, the permissions defined by the profile will override the standard permissions of the site (set under "Permissions"), but only for that specific board.
The Permission Profile section comes with several pre-set profiles, like "Read Only" and "Reply Only".
Who is allowed to see which board
In SMF, the ability to see a board is not handled with permissions. To see which membergroups are allowed to view a board, go to Administration Center > Boards > Modify Boards and click the "modify" link on the same line as the board name. To see which boards a given membergroup is allowed to view, go to Administration Center > Members > Membergroups > Edit Membergroups, choose the "modify" link on the same line as the membergroup name, and click the [Show boards] link.
Who can manage membergroup members
This is carried out in Edit Member Groups Administration Center > Members > Membergroups, which is a list of membergroups. Click on the group name to see a list of information about the membergroup, as well as a list of all its members. Click on the modify link to see additional information and settings for this membergroup. Enter the usernames those members who you want to manage the membergroup in question. These members will become group moderators, who are able to add/remove members in this membergroup.
Who can moderate single boards
If you want someone to be able to moderate one or two boards, rather than all the boards on your forum, add that member to the board moderator list by going to Administration Center > Boards > Modify Boards. This member will have all the permissions that belong to the moderators group, but only when they are working on topics in that specific board.