Looking at relativism as a reaction, we could define it as the denial of the following:

• Moral evaluations are objective in some sense. When I say objective, I mean that they have a source outside human decisions and choices.
• There is one moral truth. If two moral evaluations conflict, one of them is incorrect.
• The same morality is binding on all people (or, as some would say, on all reasonable beings).

I think this is the core of what the relativist is saying. He or she denies these more traditional claims.