This word is used once in Chapter Ten of Great Expectations to describe the kind of challenges that Biddy has to face as she attempts to teach the children who come to the school thanks to the ineffective aid given by Mr. Wopsle's great-aunt, who normally falls asleep. Dickens satirises Victorian education in this great chapter, and the sentence containing the word "refractory" is as follows:
This part of the Course was usually lightened by several single combats between Biddy and refractory students.
Refractory then means either unmanageable or obstinate or not responding to stimulation, either of which could be applied to the students whome Biddy is trying to teach. The reference to several single combats makes school sound like a gladiatorial arena, with spectators like Pip watching on with great amusement, finding entertainment in Biddy's attempts to instruct the ignorant.