"User permissions" refers to the permissions defined by modules to allow users to do specific actions defined from modules. It is different from "file permissions," which are the access permissions users have for files in a file system.
In Drupal, every user has specific permissions that are indirectly assigned to each user; each user is assigned to a role, and the permissions are assigned to the roles.
Drupal core modules define a standard set of permissions, such as "administer users," "administer content," and "view content." Third-party modules can expand the permissions by implementing hook_perm() (Drupal 6) or hook_permission() (Drupal 7).