Just as Puritans believed in the reality and existence of God, they also believed in the reality and existence of the devil. They believed that the devil existed, and that he had a powerful, direct influence on the lives of everyone on earth. Because of this belief, came the belief that witches and other forms of evil spirits existed (incubi, succubi, demons, etc.) Reverend Hale, a man of god, was also well-learned in the "demonic arts" as he calls them, and has researched and studied deeply on all of the forms and ways that devil can manifest itself in the lives of people. He was the local expert on witchcraft and other such evil possessions and influences.
Hale's expertise on the devil gave him credibility and respect in his life; he was called upon all over the place to come and visit their towns and give his expert opinion. It made him feel quite spiffy to be honest with you, that he was so revered and respected. The weight of his word carried a heavy and powerful influence; if he declared witchcraft existed, people listened and acted accordingly. Thus, Hale carried great power. It gave him a little bit of an ego, but as you will see as the play continues, in the end he is a humbled, contrite man who regrets that he so quickly jumped to the conclusion of witchcraft in Salem. I hope that those thoughts helped; good luck!