Mary Warren is about to reveal information about Betty and Abigail that might shed a negative light on him and his role as a minister of God in the town. Mary is going to tell the judges that they were caught dancing in the woods, and in order to not get in trouble for that act, lied about being prompted to do it by "witches." Her continued testimony will assert that this entire time, Abby, Betty and all of the other girls have been lying, and that the accused women are not witches at all, just victims of scheming and evil girls who didn't want to get in trouble.
Here are the problems that Parris has with that testimony. First of all, Betty is his daughter, and Abigail is his niece, who he's been caring for for years now. If it gets out that they wer liars, and have been knowingly condemning people to their deaths, that will look REALLY bad for him. First of all, it will be known that they were dancing in the woods and casting spells (all forbidden), and then it will be known that they were basically killing people in order to get out of trouble for it. So far, the fancy judges know nothing about the dancing, and Parris holds an upstanding reputation with them. If the judges discover the dancing, the judges, and the entire town, will turn against Parris and throw him out.
Secondly, Parris has been a key figure in all of the court proceedings that have occurred so far. He has almost been like another judge, being helpful and questioning people, and giving the judges necessary background information on all of the people. He has been instrumental in the accusation of many women. So, if it is discovered that the women are innocent, and that the testifiers have been lying, it will mean that Parris too is guilty by association. It will mean that he has been condemning innocent women to death also--not a good position to be in, for him.
I hope that those thoughts help to clarify Parris's position a bit; he wants to protect his reputation as a man of god who raises good children, and as a member of a court that has ousted witchcraft. Mary's testimony will undermine all of that for him. Good luck!