A duality in literature refers to two opposing parts of the same whole. For example, good and evil are the two opposing parts of human beings. There are several dualities in Dickens' A Tale of Two Cities.
The book starts by presenting a series of dualities:
"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair" (page 3).
These dualities are meant to represent the duality of the French Revolution, which is both hopeful in its intent to curb the excesses of the French monarchy, yet it also brings despair with its turn to excessive bloodshed.
At the beginning of the book, there is an explicit contrast between the duality of England and France. Dickens writes, "Spiritual revelations were conceded to England at that favored period" (page 3). Later, Dickens writes that "France [was] less favored on the whole as to matters spiritual than her sister of the shield and trident" (page 3). As France becomes embroiled in the chaos and bloodshed of the French Revolution, England remains the land of peace and a refuge from France. Charles Darnay must leave France and live in England to escape from his family's evil reputation as French aristocrats.
Similarly, Sydney Carton and Charles Darnay are also presented as dualities. They are "so like each other in feature, so unlike each other in manner" (page 54). They look so similar as to be mistaken for each other, but they are different in that Carton is disliked and disreputable, while Darnay is respected and adored (particularly by Lucie Manette). In the end, when Carton saves Darnay, Carton becomes good, and the two sides of this duality are reconciled.