In an attempt to reclaim his masculinity and find meaning, the narrator creates an alternate persona: Tyler Durden, the charismatic and aggressive leader of Fight Club. Tyler represents the narrator's repressed desires for violence, chaos, and rebellion. Through Tyler, the narrator is able to experience a sense of freedom and empowerment, unconstrained by the limitations of his ordinary life.
The central reveal of Fight Club —that Tyler Durden is not a separate person but a dissociated personality of the Narrator—is pivotal to understanding his character.
He represents the struggle to find authenticity in a world of artificiality. His journey—from a mindless consumer, to a radicalized extremist, to a man taking responsibility for his own life—serves as a cautionary tale. He shows us that creating a "perfect" version of oneself to escape reality only creates a monster that will eventually consume you.
The climax involves the Narrator realizing that he and Tyler are the same person. To defeat Tyler, he must accept the consequences of his actions. By putting the gun in his own mouth and firing (shooting through his cheek in the film, or through the neck in the book), he accepts responsibility. He destroys the idealized "Tyler" to save his own humanity and protect Marla.