What is the meaning behind the gender definitions, and what do they mean to the story as a whole in George Orwell's 1984?

This is an interesting and complex question. In the novel, we perceive gender both through the eyes of Winston, a male, and through the lens of the Party, which wants to neuter gender. 

Winston, at first, reacts hostilely to Julia, for she activates within him the sexual frustration he feels in a system that exalts chastity as a high virtue. The narrow red anti-sex sash she wears around her attractive waist symbolizes to him the way he is barred from a normal sex life with a beautiful woman. Julia is to Winston at first solely a sex object, and worse, a wholly forbidden sex object, flaunting both her desirability and her inaccessibility. He has conflicted desires: he wants to have sex with her but since she presents as frigid this causes him to engage in violent fantasies about her. Later, when they have an affair, he falls in love with her, and she comes to represent completion and wholeness to him, much of this is based on sexual fulfillment, but some of it is clearly a response to appreciating Julia as a whole person: body, mind and spirit. 

The state of Oceania wants to destroy gendered relationships of the old-fashioned type Julia and Winston represent, where a man and woman place their first loyalty at the feet of the other. This kind of relationship is obviously at odds with total devotion to the state and worship of Big Brother as the ultimate goods. To ensure they put the state first, O'Brien (or his proxy in the case of Julia) manages to destroy the trust between Julia and Winston by manipulating each into betraying the other. At the end of the book, we see Julia, particularly, as degendered in a way no red anti-sex league sash could ever accomplish: she is lumpen, thick, without a spark and beyond interest in sex. In reducing Winston and Julia to broken, degendered states, Orwell shows that the Party has won.