I've read a little bit about "dominion theology", and don't feel I understand it. What distinguishes this movement from mainstream modern Christianity?
Dominion Theology is the belief that society should be governed exclusively by Christian Laws, whether or not all of the people in that society are Christians. It is very much a minority view within Christianity, which has traditionally believed in dual secular and ecclesiatical authorities, even in times and places where Christianity has been the dominant or state religion.
For example, even at the height of Christian dominance in Europe, Kings were permitted and expected to make laws for their subjects and enforce them, apart from church law.
The name "Dominion Theology" is derived from Genesis 1:28, where God grants humanity "dominion" over the Earth.
See Wikipedia and its references for more detail.