Moral relativism is the doctrine or belief that there are NO absolutes in the universe. There is no such thing as an absolute right and wrong. There is no such thing as sin. In the end, each person decides for himself what is right and what is wrong. If that person decides that there is no such thing as sin, then for that person there is no such thing as sin. That's moral relativism.
I have encountered atheists and moral relativists who subscribe to these principles and preach these principles. This can be a very fun and entertaining group to observe, because of the hypocrisy or play-acting that they engage in, so as to make their chosen point of view believable to them.
Pick your favorite atheist or moral relativist, and then notice one very funny and important fact. Each one of these people knows instantly when he or she has been wronged, offended, or sinned against. They know it instantly and are ready to retaliate. Deep inside of each one of them is a firm and ingrained sense of right and wrong that tells them instantly whenever they are offended, wronged, hurt, or sinned against. They know it instantly.
Yet, these very same people will preach to us every day telling us that there is no absolute right or wrong and that there is no such thing as sin, meaning in fact that the rules of right and wrong and the commandments of God do not apply to these moral relativists. However, these very same moral relativists and atheists go right on believing that the rules of right and wrong and the commandments of God do indeed apply to the rest of us, especially in our relationships to these moral relativists.
The moral relativists want you to keep turning the other cheek over and over again for all eternity, while they continue to slap you in the face for all eternity. They want you following the absolutes and the commandments of God and the rules of society, while they themselves remain exempt from all of these things.
Moral relativism is a Satanic trap that the atheists fall for quickly and easily. They become a law unto themselves, while at the same time they expect the rest of us to obey the laws of the land. Observe for yourself. The moral relativists are the first ones to yell out, "That's not fair! That's not right!", whenever something goes wrong or the fates move against them. It's a fun and intersting pyschological phenomenon to observe.