Activity completion allows the teacher to set completion criteria in a specific activity's settings. . The criterion might be viewing, receiving a certain score or a student marking it as complete.
Students see a 'To do' dropdown which when clicked displays a list of what they must do to complete an item:

With edit mode enabled, teachers see a similar 'Completion' dropdown with an 'Edit completion' link taking them directly to the Completion conditions section of the activity or resource.

A teacher may mark an activity complete on behalf of a student from the Activity completion report if they have the capability Override activity completion (which is enabled by default.)