The meaning of Hester's "A" is an inevitable part of any discussion about The Scarlet Letter.
While the "A" initially symbolizes "adultery," later various people assign meanings such as "able" or "angel" to the letter, as the community's views of Hester change. For Governor Bellingham's servant, the letter signals Hester's upper-class ("aristocratic" or "authoritarian") status. Not only does the scarlet letter's meaning mutate throughout the novel, but the letter itself seems to multiply.
Warning: Spoilers ahead!
For example, Hester's daughter Pearl becomes a living embodiment of the letter, and a version of the letter has apparently been burned into Arthur Dimmesdale's flesh, whether by human or supernatural means. The letter also appears momentarily in the form of a meteor that flashes across the sky.
The mutability of the letter characterizes all of the symbols in the novel: All are ambiguous; none can be distilled into a single meaning that is the same for all people and all time.