Moral relativism holds that moral truth is indexed. "Killing is wrong" is not true simply, but true relative to a society, a framework or a person.

Three claims that get run together

Descriptive relativism. Societies have held different moral views. This is an anthropological observation and almost nobody disputes it.

Meta-ethical relativism. Moral statements are made true by the standards of a culture, so there is no framework-independent fact about which is right. This is the philosophical thesis.

Normative relativism. Therefore we ought not judge or interfere with other cultures. This does not follow from the second — and if it did, it would be a universal obligation, which is exactly what relativism denies.

Most arguments about the subject conflate the first with the second, or assume the third follows from the second.

The case for

Disagreement is deep and old, and persists among informed and reasonable people, which is unlike disputes about matters of fact. Moral views track social arrangements closely enough to suggest they are produced by them. And the alternative has to say where objective moral facts reside and how anyone detects them.

The case against

Reform becomes unintelligible. If a culture's standards determine what is right there, a reformer arguing against them is simply wrong by definition, and moral progress cannot be described as progress.

The boundaries are arbitrary. Which culture indexes the truth? Societies contain disagreeing subcultures, and people belong to several at once.

Self-application. If all moral claims are relative, so is relativism's own implied claim that tolerance is required.

The middle positions

Most philosophers accept that moral practice is culturally shaped without concluding that moral truth is. Some argue that a small set of constraints follows from facts about human beings, with wide local variation above it. Bernard Williams argued the whole debate is misconceived, because relativism is only tempting about cultures too distant to be in real contact, and irrelevant to the ones we actually confront. See ethics and is-ought gap.