For example, suppose one day Bob insults Alice, and then Alice hits Bob, and then the pair start fighting. Both Bob and Alice might be punished for "fighting" on the grounds that it doesn't matter who "started it".
Sometimes international conflicts are viewed similarly, and interested parties periodically urge both sides to conduct a ceasefire and "get back to the negotiating table". However these negotiations may prove difficult in that both parties in a conflict believe that they are morally superior to the other, and are unwilling to negotiate on basis of moral equivalence. Frequently, there will be the sense on both sides that the other person started it.
Furthermore a sense of moral superiority may come not only from the cause of the fighting but the behavior of the parties within it. Frequently, one side will consider the tactics used by the other as illegitimate, and hence their use as a sign of moral inferiority.
Generally the term "moral equivalence" is used in writing that denies that parties to conflict have the same moral standing. For example, in the Cold War advocates for the United States viewed the Soviet Union as the "bad guy" in the conflict and justified hostile, even violent American action as supporting freedom.
The importance of moral equivalence or inequivalence often is dependent on the framework used in the discussion. Nationalisms generally have a strong moral component in them in an effort to justify the aims of the nation. By contrast realist models of international relations or game theory models of behavior generally do not include judgements about the rightness or wrongness of the actors in the model.