Reputation is the way that other people perceive you. Integrity is the way you perceive yourself. Several characters in The Crucible face a tough decision: to protect their reputation or their integrity. Parris, Abigail, and others to protect their reputations. Rebecca Nurse and, eventually, John Proctor, choose to protect their integrity.
In rigid communities like Salem, a bad reputation can result in social or even physical punishment. The Crucible argues that those most concerned with reputation, like Parris, are dangerous to society: to protect themselves, they're willing to let others be harmed and fuel hysteria in the process. In contrast, The Crucible shows that those who favor integrity by admitting mistakes and refusing to lie just to save their own lives help defy hysteria. Willing to die for what they believe in, they put a stop to the baseless fear that feeds hysteria.