Here you can assign the currently edited permission to particular roles. To do so, select the site from the Site drop-down list, which will display all roles of the given site in a list below. The (global) option can be selected to configure global roles, i.e. those that are not limited to a single site. Then use the check-boxes to assign the permission to the roles.

 

To check if the permission is granted to a user, you can select the user from the Report for user drop-down list. After doing so, a sum of all permissions granted to the user's roles is displayed in the first line, highlighted in green color. Roles where the selected user is a member will be highlighted in yellow color. If you enable the Show only this user's roles check-box, only the yellow roles will be displayed in the matrix.

 

More resources on Permissions can be found in Developer's Guide -> Development -> Membership, permissions and security -> Permissions -> Permissions overview.