Dualism generally refers to something that has two distinct parts, often in opposition to each other, sometimes with related aspects. The classic storytelling convention of tragedy/comedy is dualistic in nature, contrasting humor with pathos. In Fahrenheit 451, the most obvious example of dualism is between Montag's wife Mildred, who is a pure and complete product of the modern society, and his neighbor Clarissa, who wants to move beyond the restrictions of society and live for herself.
Mildred is entirely obsessed with her status and her television programming, being almost hypnotized by the enormous screens that cover her parlor walls; she dismisses Montag's attempts to probe past accepted norms.
Clarissa shows an interest in Montag's growing unease, and speaks of individualism and her own ambitions, which stretch beyond society's expectations. Her simple nature and obvious questions give Montag the ability to look past societal rules.
Both women have major effects on Montag, but in different ways. Mildred shows Montag the benefits of remaining in society, where he will be unhappy but safe, while Clarissa shows Montag the benefits of fighting oppression, which endangers his life but allows him to expand his mind.
Dualism involves contrasts or opposites. For example, Montag's wife, Mildred, and Clarisse are opposites in the ways they live their lives, view life, etc.