The Reverend Parris and Judge Danforth have, in the course of the play, condemned, arrested and accused hundreds of people in the town of Salem of being witches. Those people are in jail; numerous others have been hanged, and their court decisions have made news and spread throughout the country. Danforth holds a proud court, meaning, one that takes pride in being right and in issuing edicts that are obeyed and powerful. He takes pride in his "logical" and supposedly fail-proof ways of judging people. We see this especially in act three when John, Giles and Francis challenge his decisions on the accused. He explains over and over again in different ways how witchcraft works, how judging the bewitched works, and is so proud that he refuses to acknowledge that they have any sense in what they are saying. So, it is evident that he is a proud man.
Add to this Reverend Parris, who upon the play's beginning, expressed himself to feel like he was underappreciated and disliked in the town. He felt he deserved more credit and fame. When the judges come in town and he becomes a very helpful and respected member of the court system, his ego is finally stroked. Also, it allows him to see many people he didn't like be accused of witchcraft--there is a sense of sweet justice in that. To top it all off, he is afraid that his household will be seen as being one that housed a witch--it was his niece, Abby, after all, that had started all the chaos with the dancing in the woods. He was terrified that his name would be associated with witchcraft. So, his zealousy in helping the courts helps to alleviate that possibility.
Then, add to that the following: if they were wrong in judging all of those people, then their careers are over--especially Danforth's. He won't ever be trusted to judge anyone again. So add to the list fear of losing your job or reputation. Lastly, at the end of the play, they hear that a neighboring town of Andover had overthrown the courts and that chaos had erupted in the town. If they are seen as wrong, then they are afraid that the people of the town will rise against them and do them harm. After all, Parris already had a knife put in his door. Who knows what else the townsfolk would do! They could be in danger of being killed! So, fear of their own lives is another factor.
I hope that those thought helped; good luck!