Moral relativism is the philosophical position which holds that there is no absolute or objective morality. The position is informed by the observation that moral codes vary greatly between groups and individuals.
Moral relativism is directly opposed to systems that advocate for moral absolutism; many of these are religiously-based moral codes, which often use their grounding in an ostensibly eternal and universal set of principles to argue that what is "right" is the same everywhere and at all times.
Thus, people whose moral sense is informed by the belief that morality was defined by God generally decry moral relativism, because it asserts that people, and not God, created the laws they live by, and there is therefore no justification for universally prohibiting actions deemed wrong within the prevailing moral principles of a given religious tradition.
 Religious moral relativism
Where the rubber meets the road, however, it is not possible to live one's life by a set of presumably "eternal" moral principles revealed in scripture. Consider slavery. Both the Old and New Testaments have specific instructions for slaves and slave-holders, and never condemn the practice. Christian leaders used to have no qualms about using the Bible to support such positions. Nowadays, however, only Christian dominionists would dare voice such an attitude.
The Roman Catholic Church has had a history of being conflicted on whether slavery was compatible with natural law: first accepting it as compatible with natural law, accepting it as necessary and good utility-wise but outside of the realm of natural law, and finally rejecting it as an unnecessary evil that is against natural law by the time of the 20th century. Church apologists attempt to dance around the issue with various claims, such as certain types of slavery being bad (and the Church was, of course, always against whatever slavery was bad), that the Catholic who claimed it may have not been a real catholic (even if it was the Pope), or that the Church has really always been against all slavery and has just "clarified" its teachings on slavery when society finally figured out it was wrong.
 See also
- Cultural relativism
- Moral absolutism
- Euthyphro dilemma
- Relativity, which is totally unrelated, but is nonetheless decried as moral relativism by some
- Entry in the Stanford Encyclopedia of Philosophy
- Jesse Prinz. Morality is a Culturally Conditioned Response. Philosophy Now, Jan/Feb 2012