First of all, he distinguishes what he calls moral principles from what he calls local rules and neutral norms.

As I understand it, he argues that top level moral principles are true by virtue of the meaning of our moral concepts. In some sense they are necessary truths. These principles are used to justify local rules and neutral norms.

Local rules and neutral norms, on the other hand, can vary with circumstances. As a result, different communities around the world can have different local rules and neutral norms, but there is only one set of moral principles. Everything depends on different circumstances.

To the extent that ethical relativism posits the existence of different fundamental or top level moral principles that are equally true or binding for different groups of people, Singer would say that it is mistaken. On the other hand, his system can account for and justify different sets of lower level rules and moral judgments because of different circumstances.