admin/roles/permissions

In Moodle, Permissions and Capabilities are terms that are often used to describe the same thing, they are interchangeable. It does not matter which term you use in most circumstances, but this is one area where there can be no misunderstanding about what does what. Experiment on your private Moodle with Permissions where you can control things, a conflict in Permissions or a changed Permission that gives someone access to things they should not have access to, can cause a number of problems for Administrators and, in absolute dire circumstances, can wreck your Moodle.

A Quick Overview of Permissions/Capabilities and Roles

Permissions are all context driven.

In this sense, "context" means that the current location of the User. This is the point at which permissions are calculated, the User is granted Capabilities that suit the Role at that point and depending on which permissions are granted at that level, the User's Capabilities will be limited by those permissions.

For example:

 At the Front Page, not logged in: No permissions are granted except the ability to log in.
 At the Front Page after log in: Depending on the "Default Role" the User may be an Authenticated User, a Student, or some other Role.
 At the Category Level: The User will usually be an Authenticated User, but may be given the Role of Administrator, Course Manager or Teacher. 
 At the Course level: Most Users will be given a role of Student, some will be Teachers, fewer will be Course Managers, and very few will be Administrators.

NOTE: Permissions for Roles are ALWAYS calculated at the place where they are given a Role other than an Authenticated User. The Role is then granted to all levels below the place where the Role is granted. In practice this means if Joan Smith is granted the Role of Teacher at the Science Category level, then Joan will be a Teacher in ALL courses in the Science Category. If John Smith is given the Role of Teacher in Physics 101, then when he goes to the Science Category, he will be an Authenticated user, and he may not enter any other course as a Teacher, until given permissions, capabilities, to be a Teacher in another course.

Roles are assigned at all levels of Moodle, and the permissions granted only apply to that User in that context.

Permissions

Permissions in Moodle 2.0 are pretty much the same as they are in earlier versions, but the layout is far more definitive.

Setting a permission

More later.