The following discussion is adapted from an interview with Summit Ministries, Manitou Springs Colorado, July 1998. Summit is a Christian educational organization training young people in Christian worldview leadership.
Moral relativism is a kind of subjectivism.
There are no objective moral rules. Rather, morality is a personal choice. Many assume that moral claims are merely preference claims. There's a difference between disliking something and thinking it's morally wrong. Of course, all morality collapses into mere preference if there are no moral rules at all.