In the prologue, Shakespeare is setting the stage for the play and introducing the main conflict. He is telling the audience that the events that will follow are a result of this ancient grudge. The feud is so strong that it has led to a new mutiny, or rebellion, between the two families. This mutiny will be the driving force of the play and will lead to the tragic deaths of Romeo and Juliet.
Shakespeare uses the word "mutiny" to emphasize the seriousness of the situation. Mutiny is a military term that refers to a rebellion against authority. In this case, the mutiny is against the social order and the peace that is supposed to exist between the two families. The use of this word shows that the feud between the Montagues and the Capulets is a serious matter and that it will have far-reaching consequences.