The main conflict in the novel is between the desires of the heart and the economic and social constraints on that desire posed by family and society.
Catherine Earnshaw and Heathcliff love each other deeply and would love to get married, but Heathcliff, degraded to a farmhand by his older stepbrother Hindley, makes that an unrealistic possibility. Catherine does the practical thing and marries the rich man in the neighborhood, Edgar Linton. Heathcliff runs off in despair and comes back after a mysterious absence of three years, having fashioned himself into a gentleman. Because of her marriage, Catherine and Heathcliff cannot be together, as Linton increasingly won't even endure Heathcliff's presence. The separation eventually kills Catherine and leaves Heathcliff in a state of grief and rage.
Several themes emerge out of this central conflict of love versus society. The first is revenge: Heathcliff is determined to revenge himself on the Earnshaw and Linton families, both of whom he blames for destroying the possibilities of love between he and Catherine. He does this by using the weapons of his society—most notably money and patriarchy—against his enemies. For example, he elopes with Linton's sister to hurt Linton and uses his patriarchal power as a husband to mistreat his wife. He uses gambling (money) to get ahold of Wuthering Heights.
Another theme is repetition: Heathcliff wants to replicate the same hurt he experienced in losing Catherine on Hareton, Hindley's son, and he does his best to degrade him. He then encourages him to love the young Cathy, meaning to cruelly separate the two.
This leads to yet another theme: healing. Heathcliff loses his will to revenge at the end and allows the healing relationship between Hindley and Cathy to develop.