The breastplate, which belongs to the Governor, is a symbol of his and the state's authority:
"This bright panoply was not meant for mere idle show, but had been worn by the Governor on many a solemn muster and training field, and had glittered, moreover, at the head of a regiment in the Pequod war. For, though bred a lawyer, and accustomed to speak of Bacon, Coke, Noye, and Finch, as his professional associates, the exigencies of this new country had transformed Governor Bellingham into a soldier, as well as a statesman and ruler."
When Hester sees herself reflected in it, she sees herself and her "A" as the state sees her: "Hester looked, by way of humoring the child; and she saw that, owing to the peculiar effect of this convex mirror, the scarlet letter was represented in exaggerated and gigantic proportions, so as to be greatly the most prominent feature of her appearance."
This short incident reminds us of how officialdom sees Hester; it is not how the population sees Hester as she begins the transformation from adulteress to "Able" or "Angel."