What special knowledge does Hester feel the Scarlet Letter gives her?

Whereas at first it represented Hester's adultery and her needlework skills, it now takes on two more meanings. First, the letter begins to represent the hidden shame of the community. Preachers stop in the street and address their fiery words towards Hester, and she becomes a lightning rod for all sin, for all the latent build-up of repressed rage fomented by the strict morals and codes of the society. The more the community unloads its hatred and judgment upon Hester, the more it can use her as an example or deterrent in the name of eradicating sin.

Hester also can sense when people sympathize with her, perhaps because of their own secret sins. Thus the letter serves as a gateway into other people's secret crimes, and it acts as a focal point for the shame of the entire community. The letter thus can be interpreted as a symbol of shame shared by everyone rather than by Hester alone.

Sometimes the red infamy upon her breast would give a sympathetic throb, as she passed near a venerable minister or magistrate, the model of piety and justice, to whom that age of antique reverence looked up, as to a mortal man in fellowship with angels. "What evil thing is at hand?" would Hester say to herself. Lifting her reluctant eyes, there would be nothing human within the scope of view, save the form of this earthly saint! Again a mystic sisterhood would contumaciously assert itself, as she met the sanctified frown of some matron, who, according to the rumour of all tongues, had kept cold snow within her bosom throughout life. That unsunned snow in the matron's bosom, and the burning shame on Hester Prynne's--what had the two in common? Or, once more, the electric thrill would give her warning--"Behold Hester, here is a companion!" and, looking up, she would detect the eyes of a young maiden glancing at the scarlet letter, shyly and aside, and quickly averted, with a faint, chill crimson in her cheeks as if her purity were somewhat sullied by that momentary glance. O Fiend, whose talisman was that fatal symbol, wouldst thou leave nothing, whether in youth or age, for this poor sinner to revere?--such loss of faith is ever one of the saddest results of sin. Be it accepted as a proof that all was not corrupt in this poor victim of her own frailty, and man's hard law, that Hester Prynne yet struggled to believe that no fellow-mortal was guilty like herself.