It means to have dominion over them which means to have the power to control them and not be overruled by them. Many animals are more powerful in pyhsical abilities and would defeat men in "hand to paw" combat. But God gave man a mind to have control over matter!
It means the same thing with Jesus having dominion over mankind. We will worship Christ and not the other way around. We will be subject to His rule and our mind won't matter because His Love will be without limits.