The interesting thing about Katya is that for much of the novel she is a blank face. She's more or less a two-dimensional character, confined to the background, until Arkady returns to Nikolskoye. When Arkady recognizes that he is in love with her, she suddenly gets more space in the narrative and it's as if she bursts into a third-dimension.
Initially, Katya comes across as a child. Arkady thinks of her only as a consolation for not being able to spend time with Anna Sergeyevna, and the two of them more or less develop a friendship in spite of themselves. The narrator describes her as "still innocently fresh," and she often blushes around her sister and Bazarov (16.19). It is perhaps her innocence that attracts Bazarov to her. Since he prefers conquests to deep romantic relationships, the younger sister, who seems less challenging than Anna Sergeyevna, holds a certain appeal for him.
Katya blooms into a full character when Arkady returns to Nikolskoye and the two of them take a walk in the garden. She is the first character to admit indifference to Bazarov, the first character to admit that she simply has nothing in common with him. She tells Arkady, "He's a wild beast, while you and I are domestic animals" (25.20). Arkady is offended at the thought, but, as time passes, he begins to realize that she is right. In Katya's view, which may well be correct, Bazarov is gripped less by an idea than by a certain intensity that he cannot control.
It's Katya who opens up the possibility of happiness for Arkady, who gets him thinking less about what he will become and more about a quiet domestic life. Yet she is not all modesty. She admits that she is proud, in her way, and that she doesn't like the idea of marrying a rich man because she doesn't want "a mere subordinate existence" (25.67). Perhaps part of what attracts her to Arkady is his very meekness. She knows that she will not be entirely dominated by her husband, that she can still play a role in the household.
The closest thing we get to a character flaw in Katya comes when Anna Sergeyevna finds her sitting alone in the garden after Arkady has confessed his admiration for her. Anna Sergeyevna tells her to take better care of her feet because they are so pretty. Katya thinks, "Pretty little feet, you say... Well, before long he shall be kneeling at them" (25.93). Though Katya feels ashamed a moment later, this burst of vanity makes her a much deeper and more interesting character.
Even though we have heard her express strong opinions to Arkady, she still might seem too simple and good to be a full character; it's as if all the complexities are reserved for the men in the novel and for the unusual Anna Sergeyevna. It's this moment of weakness that brings us readers closest to Katya, and makes us sympathize with her; she may be exceptionally good and kind, but she has flaws and complexities just like everyone else.