The "Old Boy" line appears in Act I of The Crucible, and the line is spoken by Reverend Hale.

"We shall need hard study, if it comes to tracking down the Old Boy."

The "Old Boy" that he speaks of is the Devil (Satan). There is a small suspicion of witchcraft in Salem, and Parris requests Hale's presence to confirm that witchcraft is actually not present.

"There be no unnatural causes here. Tell him I have sent for Reverend Hale of Beverly, and Mister Hale will surely confirm that."

Hale has built himself a reputation for having quite a bit of experience rooting out "demonic arts." Hale shows up, and he has a lot of very heavy books with him. Parris comments on their weight, and Hale states that they should be heavy because they are weighted with God's authority. Parris then comments again about the books, and he says that Hale has come quite well prepared. Hale confirms this notion by saying that he and others will have to study hard to track down the "Old Boy" (Satan) and root him out of Salem. Considering the very real fear the Puritans have of Satan and demonic forces, it is quite surprising that Hale refers to the Devil in such a familiar and nonchalant manner. Between that comment and his comments about his books, Hale is presented to audiences as overconfident and a bit pompous.

The "Old Boy" is the Devil himself. The Reverend Hale has come to Roanoke to assist Parris in figuring out what has happened in his parish.

Hale has come with an armful of religious texts "weighted with authority." The remark is simulateously pompous and patronizing. To call the Devil the "Old Boy" is pompous because he is not exercising proper respect for the task at hand, should his belief in Satanic powers be real. It is patronizing because it is like a pat on the head to Parris, making him feel lesser because he is not able to handle a problem so obviously solved, given the right person with a proper spiritual education.