This doesn't mean that we go about bragging, as one famous televangelist does, that demons flee in terror when we come into town. It also doesn't mean we should practice exorcism on everyone who has a problem. It simply means that as children of God Satan does not have dominion over us. He may have dominion over a lost soul and we have the right to pray for their deliverance and command him to depart. We may or may not see results.
Deliverance depends on more than our authority.
God does not force people to serve Him, to reject sin, or to desire deliverance, neither can we. Sometimes the person has a valid, physical, problem with their brain. In that case they do not need deliverance but healing. I have seen some zealous individuals who attempt to cast out demons in these types of situations to the shame and harm of the individual they perform this offense upon. We need to recognize that we have only as much power as God allows us to have in every situation, not the power we want and demand.