What does it mean that Hester has "Cast away the fragments of a broken chain"?
A fine question. Hester, and all women at this time, were bound to society's expectations. This binding took the form of social expectations, internalized judgments, codes of ethics, explicit preaching in sermons, and even laws. These are the chain that Hester seeks to cast aside: those fragments that she still carries in her mind and heart. This is bittersweet, because while this is meant to be a sign of freedom, many of the chains that bound women are considered positive: male approval, social approval, marriage, etc. Hester has to cast aside these "links" too.