In my opinion, Danforth's basic attitude is that he cares more about how the court and government will end up looking than about anything else. He does not really care about justice or about witches, he cares about making himself look good.
This influences the trials because it influences him to make decisions based only on the image of the court. So he ignores the fact that the girls seem to be lying. Once he has believed them, he has to keep on believing them so that he does not end up looking bad.
Danforth came off as an arrogant individual based on some of his personal remarks. He was proud of the number of people he had convicted and condemned to death. According to him, the number of condemnations made was a sign of prestige, and the Salem witch trials offered him an opportunity to add to his list. The proceedings were an opportunity for him to continue asserting his authority as an official of the court, and also to protect the reputation of the institution he represented. He was only concerned with the court's superiority over the community and his own standing as a renowned judge. His bias forced him to only believe the girls, and even when it emerged that they had lied to the court, his pride stood in the way of him making the right decision. Parris informed Danforth that Abigail had stolen some money from him and that she and Mercy Lewis had left town. However, Danforth still went ahead and hanged Rebecca Nurse and John, among others.