A divine right monarchy is one in which the monarch claims to rule by the divine right of kings. In other words, this is a monarchy in which the rulers claim that they have the right to rule because God gave that right to them.
In terms of the actual working of the monarchy, there is not necessarily any difference between a monarchy that claims the divine right and one which does not claim that right. However, monarchs who took the idea of divine right seriously often tended to be very absolutist in their outlook. This meant that they were not willing to allow any serious power to be shared with a parliament or with any other body.