From an ethicists standpoint...

Moral relativism is simply the position that the truth of a moral claim is dependent upon the belief of either the person (individual relativism, sometimes referred to as subjectivism) or the majority of a culture (cultural relativism).

Let's say Sally has an abortion. Under individual relativism if Sally believes abortions are okay, then there is nothing wrong with what she did. It doesn't matter what anyone else, nor the majority of the culture she is within believes. Under cultural relativism if the majority of the culture believes abortion is okay, then what she did is okay. However if the majority believes abortion is wrong, then she acted immorally.

As a side note, relativism in a moral sense is distinct from relativism in a anthropological sense. Anthropologically relativism is just committed to the idea that different cultures have different beliefs, e.g., Culture A believes abortion is murder while Culture B believes abortion is okay under certain circumstances.

I've been thinking about this recently because I don't think I have a good understanding. I feel like I understand the textbook definition but not how it applies to real life. It's generally defined as "understanding that morality is not fixed/objective, is malleable, and changes throughout time/cultures" etc, however, I feel like I often get roped into a discussion wherein a party is trying to convince me that if I think someone from Culture A is being immoral AT ALL then I can't possibly adhere to moral relativism. I believe that you can accept that different cultures have different means of measuring morality without FINDING those things moral. You can observe their units of measurement without adopting them, if you will.

The absence of moral absolutes or absolute morals. Also the opposite of objective morality.

For an entertaining read that looks at this question from the standpoint of mid-century philosphers, see "Metaphysical Animals"

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