What is meant by the title "the minister`s vigil"?

This chapter deals directly with Dimmesdale's desire for forgiveness and absolution. He stands vigil hoping to make up for the time he refused to stand by Hester's side.

"Dimmesdale ventures to the scaffold at night, perhaps unconsciously seeking absolution. Perhaps he believes that if he stands in the same place Hester did, he can find some degree of peace without having to publicly confess. But it is not enough. Dimmesdale already knows of his own guilt and susceptibility to sin. What he cannot make peace with is the guilt of having preached all these years to a congregation he has betrayed with his own behavior. Whereas Hester wears a scarlet letter on her clothes and has not taken it to heart, Dimmesdale's scarlet letter is hidden, and it is slowly becoming inextricable from his flesh."