What are the characteristics of Feminist theory in The Scarlet Letter?

While it's much more complicated than the following summary will allow for, Feminist critical theory generally seeks to describe and illustrate the specific experiences of those who identify as women, and especially examines how those experiences have been marginalized by a misogynist society. In other words, Feminist literary theory seeks to understand how literature has marginalized the writing of women, and how literature can play a role in breaking down the power dynamics of traditional gender roles and stereotypes. Of course, there is much more to Feminist literary theory, but those are some of the main points. 

Nathaniel Hawthorne's The Scarlet Letter is especially well-suited to Feminist literary theory. For instance, the novel explores the ways in which Hester Prynne is ostracized and condemned for having sex and giving birth outside of marriage. A Feminist critic might see this detail as exemplifying the restrictions the larger, misogynist society places upon women, and especially on female sexuality and the ways women form relationships. As such, the novel can be read as having a very strong Feminist message indeed, as it ultimately shows Hester resisting and overcoming the marginalization and oppression society has leveled against her.