Moral equivalence is the claim that two radically different ethical actors are really doing the same thing and that they should be judged and treated the same way. For example, if two schoolchildren are scuffling and hitting each other in the playground, a judgment of "moral equivalence" by the teacher may result in separating the two and (perhaps) punishing them both equally (for "fighting").
The problem with moral equivalence as an ethical doctrine is that it completely sidesteps the crucial issue of right and wrong; see good and evil. If one of the children in our example was a notorious school bully, and the other child was fighting back in self-defense, then it would clearly be wrong to punish them both equally.
If we believe that evil is defined by taking advantage of another person for one's own benefit, then an aggressive move (like a schoolyard bully beating up a little kid) is an evil action. It is clearly wrong.
Moral equivalence is ideologically similar to Einstein's Equivalence principle.