Dominion in its simplest form is power, authority or control over something or someone. It is the ability to request or command and expects a fulfillment of that appeal.
To have dominion is to rule, to be in charge. Dominion is a command or authoritative order that put other forces under. The above verse clearly teaches that dominion has been given over the plants and animals and the earth, which mankind must enforce [Ps. 8:6-9, Heb. 2:6-9].
Man was created in the image and likeness of God on planet earth so that he can bring all that heaven is and has to earth the newly created territory where man has been capacitated to rule as delegated authority or ambassador of God. All that is on earth was designed to reflect or look like the kingdom of Heaven. Alongside this dominion he was given a mandate, a task to do, and a responsibility.
Mandate is an official order or commission to do something; it is the authority to carry out the dominion policy as instituted by the giver of the dominion. In the present context it is both a verbal and written authorization given to men by God to act in His stead on planet earth.
It is an official command and it is the power to act as God’s duly recognized delegated power on earth.
One very important mandate given to the New Testament saints is to bring people out of darkness by translating them into the kingdom of His dear Son where light dispels darkness.