Hale denouncing the proceedings because of the testimony and evidence against the girls, specifically against Abigail by Proctor, showing that the girls are faking and that witchcraft has nothing to do with anything. As more and more upstanding members of both the town and the church are arrested, Hale becomes more and more skeptical of the validity of the girl's actions. Because of his authority as a clergymen and expert on witchcraft, his declaration that there were no signs of witchcraft should have been respected, and the trials put to an end. However, because of the pride of the leadership in Salem, and because they would not admit that they had committed any wrongdoing in accusing others, the courts did not relent. This resulted in the deaths of dozens of innocent people.
Hale is a traveling minister brought in to Salem at the very beginning of the town to assess whether or not witchcraft has taken some of its residents. Hale is an interesting character because he is dynamic, meaning he makes quite a transformation from the beginning to the end of the play. At the beginning, the text states that Hale travels toward the village as a "tight-skinned, eager-eyed intellectual" and as someone who felt "pride of the specialist whose unique knowledge has at last been publicly called for." When he first appears to the other characters, he is "loaded down with half a dozen heavy books." We can see from these descriptions that Hale is a serious, learned man when it comes to witchcraft, and our modern knowledge of these accusations leads us to believe that, while Hale has unselfish intent, he and his "studies" are catalysts for the deaths of many innocent people. We see, in fact, in the first couple of acts that Hale asks leading questions and cannot prove witchcraft: his "interview" with Tituba at the end of Act I is almost comical in the ridiculousness of his questioning ("When the Devil comes to you does he ever come -- with another person? Perhaps another person in the village? Someone you know?").
However, in Act III, Hale denounces the court proceedings because he finally sees that the girls are lying. He observes the girls in their witchcraft act, pretending to see a bird that isn't there and pretending to be freezing cold. When Elizabeth lies to protect John, Hale understands that "it is a natural lie to tell" and realizes that neither John nor Elizabeth are witches. By denouncing the court, he is publicly saying that he is against the happenings in the court, and that he discredits them completely.
What should have happened with this denouncement is that the accused are released and the girls taken in to custody themselves to stand trial for the deaths of all those hanged; however, we learn in Act IV that this is not the case at all. In fact, when Hale pleads that those jailed are all released, Danforth states, "I cannot pardon these when twelve are already hanged for the same crime. It is not just." The irony here is huge - Danforth cannot release those the minister finds innocent because he has already hanged 12 others. This is the reason why Hale's denouncement means nothing: the court of Salem cannot admit its wrongdoing, so it continues to hang the accused.
It should be noted that Hale makes a major transformation from the man who first walked toward Salem, a man who believed all answers could be found in a book.