The overture of "The Crucible" provides relevant and interesting background information on the events that occurred during the Salem witch trials. Miller gave us a history of the events, along with crucial information on the mindset and attitudes of the Puritan people at this time. If we didn't have this information, we might read through or watch the play itself and think that these were just a bunch of crazy people, and dismiss the events as that. Instead, Miller helps us to understand that the Puritan people at this time had a dangerous combination of beliefs: a thorough belief in the actual existence of the devil and his influence through witchcraft, and, no way to atone for or purge their sins and grievances. Because people did and felt bad things all of the time, they felt guilty for it, but the Puritans had no confessions, or atoning for those sins, or a way that they could work out those sins in a healthy way. So instead, they had to let them fester. That festering, in combination with their belief in the devil, combined to create the trials. It provided a place for people to openly confess their sins (for example, Abby confessing that she "laughs during prayers,") and not be held accountable for those sins through blaming them on the witches and the devil.
Miller, in providing that necessary background information, helps us to understand why so many would so cruelly accuse their neighbors of crimes that they didn't commit. The overture also provides information on their culture, society, beliefs, religion and the lead-up to the trials themselves. It is very useful information that Miller has provided--background research that often we don't get with plays. I hope that those thoughts helped; good luck!