
Ryan S. answered 03/29/19
PhD in Philosophy with expertise in moral philosophy
Cultural relativism is a metaethical theory. It claims that the ONLY moral standards that exist are the various moral codes that people hold across cultures. There is no objective, universally valid moral standard that applies to everyone and that we can use to evaluate the various moral codes that people hold across cultures. Morality is thus "relative to culture" in the sense that there's no objective moral standard that we can use to evaluate the morality of our actions; there are only the moral standards that vary across--or are relative to--cultures.
Adherents of this view MIGHT take the extra step and claim that, because morality is culturally relative, we should not criticize the moral codes of other cultures. It's important to note that this conclusion is not a metaethical claim--it's not a claim about the existence of moral standards--but rather a normative claim, or a claim about what we OUGHT or SHOULD do. It's also important to recognize that cultural relativists don't have to go beyond the metaethical theory described above and embrace this extra, normative claim. It certainly doesn't follow from the fact that morality is culturally relative. At best, the idea that morality is culturally relative implies that you should not criticize the moral codes of other cultures if (and only if) the moral code of your culture forbids such criticism. At worst, it's absurd for the cultural relativist to embrace this normative claim along with their metaethical theory because the normative claim looks like it presupposes an objective moral standard--a standard that says, to everyone, that they shouldn't criticize the moral codes of other cultures--even though such a standard, according to the metaethical theory, doesn't exist.
James Rachels has a good discussion of Cultural Relativism in his The Elements of Moral Philosophy.