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.