The Reverend Parris is one of the most despicable characters in The Crucible by Arthur Miller because he ia a man of God of whom we have a right to expect better. From the beginning he demonstrates his excessive concern for himself and his reputation; those are the things he cares about, even more than his daughter's welfare. He knows the girls were dancing in the forest last night (because he was there and saw them--and no one quite knows why he was in the forest that night) and is worried about witchcraft only because of what people will think if it is discovered that his house is the center of the trouble.
In act one when he talks to Abigail, his niece, he tells her she should know he has enemies. He says,
"There is a faction that is sworn to drive me from my pulpit."
Later in the act he gets in a heated argument with Proctor and Giles over money (not surprisingly, he thinks he should get more) and he finally blurts:
"There is a party in this church. l am not blind; there is a faction and a party."
These interactions clearly demonstrate that Parris is both rather paranoid and ready to place blame on anything other than himself.
In act three, Proctor has come before the court to tell the truth--something Parris cannot bear to have told. While Parris is not an official part of the court proceedings, he is clearly intricately involved with them. Until now, the judges have had no reason to suspect Parris of hiding anything or the girls of lying. Proctor, Giles Corey, and Francis Nurse have now come to the court to expose the truth about the girls and Parris is desperate not to have that truth be told.
Proctor simply tells the truth: Abigail told him that the girls were playing in the forest, Parris caught them, and now they are just playacting about witchcraft in order to avoid punishment. This is a truth Parris knows will be damaging to him.
What Parris does, then, is try to deflect the judges' attention away from what Proctor is saying by alleging that Proctor is only here because he hates Parris and is trying to damage his reputation ("blacken his name"). He even goes so far as to say that Proctor has been trying to ruin his reputation ever since he arrived in Salem. While that was undoubtedly not Proctor's purpose, it is true that he has not been happy with the worldly and selfish preacher.
When that deflection does not work, he accuses Parris of just trying to stir up trouble.
"He’s come to overthrow this court, Your Honor!"
In short, Parris is a despicable coward who is willing to allow innocent people to be killed in order to save his own reputation. This statement is just one more attempt to deflect blame from his own role in these proceedings.
He means that Proctor is trying to make him look bad. When Parris says that Proctors is blackening his name, he means that he's saying things about him to get people not to like him. We know that Proctor does not like Parris one bit, because he tells his wife Elizabeth that Parris talks more about money than he does about God.
Hope this helped!