What influence on events do the occurrences at Andover bear?
The witch trials taking place in nearby Andover have resulted in rebellions. Parris in Act 4 says, "But the rumor here speaks rebellion in Andover," though Danforth contradicts him and says that a rebellion is not taking place in Andover. Parris persists, however, and says that the court has thrown out the witch trial cases in Andover and that a group in Salem has been watching the events in Andover and will cause a "riot." In other words, people in Andover have turned against the witch trials, and the authorities worry the people in Salem will catch this contagion and turn against the witch trials.
The events in Andover have made Parris nervous, and they are starting to make the authorities feel desperate to convince one of the accused people in Salem, such as John Proctor, to confess his guilt. In addition, the events in Andover have in part resulted in Abigail Williams's disappearance. She flees, along with her friend Mercy Lewis, and is not available to testify in court.
Basically, the events in Andover are making the people in authority in Salem worried. They have heard that the people in Andover have rebelled against the court there. They are worried that something similar might happen in Salem.
In particular, Rev. Parris is worried about this. He thinks that the next group of people scheduled to hang will cause problems. These include Rebecca Nurse and John Proctor. Unlike other people who have been killed, these two are respected by everyone in the community. Parris is afraid that if they are killed, the people will rise up against the court like they did in Andover.