When Mr. Hooper is on his deathbed, he looks all around him at the spectators who have gathered. He asks why these people tremble when they look at him when they should be trembling at the sight of one another instead. He finds it ironic that the veil — just a small piece of fabric — makes him seem so terrible, prevents people from taking any pity on him, and compels children to flee from him, as each person in the room also wears a figurative, unseen veil. Mr. Hooper says,
When the friend shows his inmost heart to his friend; the lover to his best beloved; when man does not vainly shrink from the eye of his Creator, loathsomely treasuring up the secret of his sin; then deem me a monster, for the symbol beneath which I lived, and die! I look around me, and lo! on every visage a Black Veil.
The veil itself is just a symbol. It isn't intrinsically terrible; rather, what it represents frightens people. The people fail to realize the veil's symbolism and fear the veil instead. This is important because Mr. Hooper finally confirms the veil is a symbol of each person's "secret [...] sin," as well as the way we try to hide our sinfulness from everyone else, even our closest friends, spouses, and God. We have many clues about the veil's meaning before now, but Mr. Hooper finally verifies its meaning in these lines.