Common meaning:

A person who believes they are better than other people and says so.

Hidden meaning of the Equity religion: 

A person who is part of the dominant group that takes on the values of the system that benefits them.

Discussion:

The Equityists believe that all members of a dominant group have unconsciously taken on the values of the current dominant hegemony. Their motivations are suspect because they benefit from the current system of oppression.

The problem with this kind of thinking is that it attributes everything to oppression and fails to consider that sometimes things are done a particular way simply because those values or procedures work better in the real world.

Equity declares that you have oppression anytime we are able to divide humans into two groups based on a particular characteristic. If you are a member of the majority group, then you have internalized dominance for that characteristic. For example, if you are right-handed you benefit from that and secretly hate left-handed people.

It is true there are times that one group harms another one, but internalized dominance is not a thing.