This allows a user to assign roles in a given context (system, front page, course category or course).
Note that to assign a role A to another user, the user doing the assignment has to hold a role B so that role B is permitted to assign role A. This is controlled in ‘Allow role assignments’ in Settings > Site administration > Users > Permissions > Define roles. This is logical because even though a teacher might have moodle/role:assign, in most situations we only want them to be able to assign users the student role, and not the manager role in their course.
This capability is allowed for the default roles of manager and teacher.