The difference between moral absolutism and moral relativism is the difference between saying that some things are right or wrong in all times and in all places and saying that things may be right or wrong in some times and places but not in others.
In moral absolutism, we say that there are absolute truths about what is and is not moral. For example, we might say that it is always immoral to kill another person when you are not defending yourself or some other person from serious harm. As another example, we might say that it is always wrong to enslave other people. We are making those claims without any exceptions. That is moral absolutism.
Moral relativism takes a different approach. It argues that there are no absolute truths about morality. Instead, moral rules might apply in one culture or one time in history but not in others. Actions are only right or wrong if a give society says that they are. So, to use one of our examples from the previous paragraph, it would have been moral to keep slaves in Ancient Rome or in the American South because those societies did not believe that slavery was immoral.
Moral absolutism, then, says that things are or are not moral regardless of what a particular society thinks. Moral relativism says that morality depends on the attitudes of a given society. Please follow the link below for a more detailed discussion of this issue.