In Chapter 12 of The Scarlet Letter, while Dimmesdale, Hester and Pearl are standing at night on the scaffold, Dimmesdale having asked the other two to join him there after the pain he bears made him cry aloud, a meteor splits the sky and leaves a trail in the shape of letter "A." It is interpreted by the three on the scaffold as a reference to Hester's scarlet letter. The next day the church sexton tells Dimmesdale, after handing him his glove that he dropped at the scaffold of public shame, that many townspeople are reporting the sight of a meteor that left a trail in the shape of a letter "A."
Dimmesdale is relieved and surprised to hear that the townspeople are attributing the miracle of the letter "A" in the sky to be an "A" for angel as a sign of a heavenly reward for Governor Winthrop, who died during the night at about the same time as when Dimmesdale had stood alone on the scaffold before asking Hester and Pearl to join him as they were returning from Governor Winthrop's death bed; Hester had been requested to sew his burial robe.
The red A in the sky is obviously just some kind of natural phenomenon, such as a meteor tail. In the Puritan world, these kinds of natural occurrences were seen as portents or omens.
When Arthur looks in the sky and sees the reddish vapor cloud (or whatever it was), it is his guilty conscience which causes him to see a huge scarlet letter of shame. On this busy night others, apparently, saw the same A-shaped thing in the sky. Though they saw the same physical outline or shape, they gave an entirely different meaning to the sight. Because their beloved Governor Winthrop had died, they saw the A as a recognition of his now being an angel in heaven.
The other townspeople believe it stands for Angel because Governor Winthrop just died, and he was like an angel.