The conversation to which I assume you are referring happens in the first scene of The Crucible by Arthur Miller, and it is exceptionally significant because we hear the truth (or most of the truth) about what happened to cause the tragic happenings now known as the Salem Witch Trials.
The Reverend Parris's daughter, Betty, will not move or respond to anything this morning, and the minister is gravely concerned; however, what we learn is that he is most concerned about the potential damage this incident is going to be on him and his reputation.
Everyone has begin to talk about witchcraft, and the reverend has even sent for an expert, Reverend Hale, to come and confirm that there is no witchcraft here in his town--and certainly not in his house.
No - no. There be no unnatural cause here.... I have sent for Reverend Hale of Beverly, and Mr. Hale will surely confirm that. Let him look to medicine and put out all thought of unnatural causes here. There be none.
He seems relatively calm in front of others, but when he and his niece Abigail Williams are alone, he directs his fury at her.
Parris, pressed, turns on her: And what shall I say to them? That my daughter and my niece I discovered dancing like heathen in the forest?
This is huge. Not only do we learn that Betty, Abigail, and the other girls were dancing in the forest last night, but we learn that Parris was there and he knows they were doing something they should not have been doing. (By the way, what was Parris doing in the forest last night?) He has to know that what is happening to Betty is a just reaction to that incident in some way.
Parris rants for a time about "a faction" of his congregation who is out to get him (which suggests at least some degree of paranoia on his part) and then admits he saw at least one of the girls dancing naked in the forest last night. (Again, what was he doing in this place where he claims "abominations" happen?)
We learn several things from Abigail in this conversation, as well. She admits:
We did dance, uncle, and when you leaped out of the bush so suddenly, Betty was frightened and then she fainted. And there’s the whole of it.
There is the truth. Betty is not sick or bewitched; she is frightened that her father will punish her severely because he knows she was out in the forest last night. This grave untruth is the cause of so much of the grief this town will soon face.
When Parris asks her about her reputation, about whether she has committed any acts of impurity, Abigail gets irate. She claims:
My name is good in the village! I will not have it said my name is soiled! Goody Proctor is a gossiping liar!
Now we have a hint about Abigail's true motivation for the forest activities as well as her own personal desires. Trouble is brewing, and Parris and Abigail are at the center of it--and this conversation proves it.