Because of the Puritan setting of The Scarlet Letter, the adultery that bore Hester a child is the most important circumstance. In that age, the concept of adultery was one of immense sin and crime, and was looked on as almost unforgivable by society. The second most important circumstance is the identity of Hester's lover: the young minister Dimmesdale.
"People say," said another, "that the Reverend Master Dimmesdale, her godly pastor, takes it very grievously to heart that such a scandal should have come upon his congregation."
"The magistrates are God-fearing gentlemen, but merciful overmuch,--that is a truth," added a third autumnal matron.
(Hawthorne, The Scarlett Letter, eNotes eText)
Bad enough that Hester has borne a child outside of marriage, but for that child to be the daughter of a minister, one who is bound to enforce the law and religion of the time, is extraordinary indeed. In fact, because of the incredible stigma -- and lawful retribution of the town -- that would come from a confession, Dimmesdale keeps silent and allows Hester to suffer alone. However, they both know that if he confessed, the consequences for both would be severe.