Moral Relativism is the belief that there is no absolute truth on which you can base your system of morality. To quote The Life of Brian
, "you just have to figure it out for yourselves". Moral relativists have a cultural and personal sense of right or wrong. Yet they accept that other people may have different ideas.
Practical speaking a moral relativist accepts the fact that different cultures, and even different people, have vastly different ideas on how people should act. Although many cultures throughout history have claimed to have absolute truth, no culture has any objective way to prove that their ideas are better than every other set of ideas.
In contrast, a moral absolutist believes that their opinions on right or wrong represent an absolute truth. They believe that their opinions are the one true set of opinions. A moral absolutist will assume that any other person (or cultural) who disagrees with them is wrong by definition.
In my opinion, moral absolutism, which tends to have trouble accepting differences of opinion, is far more dangerous than moral relativism. The worst atrocities in human history were committed by moral absolutists.