I believe all of the above.
Supervision is simply the method that adults use to help in protecting children from injury or other harm. Supervision is an ongoing process, that is it doesn't end. It involves watching, listening, interacting, monitoring kids irrespective of where they are.
According to the American Academy of Pediatrics, “active and positive supervision” involves:
Being aware of and scanning for potential safety hazards.
Standing in a strategic position.
Scanning play activities and circulating around the area.
Teaching children the appropriate and safe use of each piece of equipment (e.g., using a slide feet-first only and teaching why climbing up a slide can cause injury, possibly a head injury).
In most situations, a supervisor should use both direct and active supervision, that is the supervisor should be able to see and hear all preschool children at all times. This includes indoors, outdoors and nap times.