This quote from Danforth to Reverend Hale is found in Act Four, scene one of Arthur Miller's The Crucible. Both men are in the jail early in the morning on the day John Proctor and the others are going to be hung. Hale is here to prevent the deaths of these innocent people, and he tries several tactics to accomplish this goal.
Before he talks with Danforth, Hale talks to the prisoners and is discouraged, but not surprised, to learn that "they will not budge." His next strategy is to try to convince Danforth to postpone the hangings for a week. This move would make him look like a hero to the townspeople, as it demonstrates mercy (and the town, by now, is sick of so many hangings).
Danforth is prideful and stubborn, and he flatly refuses. This is when he says:
"Mr. Hale, as God have not empowered me like Joshua to stop this sun from rising, so I cannot withhold from them the perfection of their punishment."
This is not a surprising thing for Danforth to say, as just a few moments before this he told Reverend Parris that "[p]ostponement now speaks a floundering on my part." Clearly he is more concerned about his own reputation in this matter than he is about the lives of Proctor and the other innocents.
The significance of Danforth's unwillingness to "withhold from them the perfection of their punishment" is that, by allowing these innocent people to die without lying to save themselves, he has ensured that they are going to die "perfectly," without a false confession on their lips. His reference to Joshua clearly indicates that he believes he is doing God's work, just as the great man of God did. Danforth believes he is the final arbiter of life and death; however, his unwillingness to bend in this matter allows Proctor and the others to choose a death in which they are at peace with their God.