This is a very natural occurrence on some species of trees and more so if the climatic conditions are suitable for the formation of aerial roots. These roots grow above ground and in air only but that air needs to be highly humid to allow the roots to form and grow. They can be used as anchors to fix the plant in place or to a rock providing additional support.
They can be formed as a method of absorbing additional nutrient and moisture. They are referred to as adventitious roots and provide an excellent opportunity for air layering for bonsai if already present. Look forward to the follow up from Derek as too what he did next with this Privet.