The main conflict in this novel is plainly suggested within its title. It is pride and prejudice vs. the success of Elizabeth's and Darcy's romance. The pride is Darcy's. His arrogant and insulting demeanor at the outset arouses Elizabeth's prejudice, causing her to eagerly accept any bad report about him (such as that which she hears from Mr. Wickham) and reject his initial confession of love. This conflict later begins to approach resolution when Elizabeth gets over her prejudice, seeing Darcy for what he really is and becoming fond of him. It is finally resolved when Darcy overcomes his pride and approaches Elizabeth with a second confession of love.
Austen's novels often suggest strong themes in her titles, occasionally including two seemingly opposing concepts against one another, such as "pride and prejudice" or "sense and sensibility" (also titles of two her best-loved stories). But ultimately the two concepts end up existing alongside of each other and working in tandem to win the day (and, often, to cement whatever potential romances are struggling to manifest). In this novel, "pride" is a pervasive theme that applies to many of the characters: Elizabeth herself, Mister Darcy, her sister Jane's suitor, her mother, and her younger sister, Lydia, as well as Mr. Collins, Mr. Wickham and others. Pride is seen as a generally positive attribute that can inadvertently lead to difficulty when it overshadows compassion and sympathy.
Prejudice is also pervasive, as when Elizabeth mistakenly assumes Darcy is prideful because he is arrogant and cold-hearted, instead of understanding his standoffish and judgmental attitude is borne of having been betrayed and annihilated by others whom he sought to help. This idea of prejudice accounts for several of the novel's characters judging others' behavior too harshly when only considering one example or instance, instead of the whole picture.
The central conflict appears to be the one that keeps Elizabeth and Darcy apart. She suspects him of being too proud and of having unreasonably-high expectations of others, and mistakes his cautious and discriminating social behavior for cruelty. He understands that she is misjudging him, but he is too proud to set things right by explaining his behavior. She in turn is too proud to allow a cruel man to woo her, despite her attraction to him. When she learns from others that Darcy's actions are more often borne of sympathy and generosity, she begins to see he is more complex than she had previously thought, and allows the positive opinions of others to sway her prejudice. In this way she relaxes her proud stance and becomes open to his attentions; he, in turn, swallows his pride and once again asks her to reconsider. They finally arrive at a point where they can express their true feelings, once the initial prejudice born of pride is swept away.