Throughout the course of the novel, Katniss changes in some very interesting ways. First of all, she becomes a lot more wary and suspicious. Instead of simply trusting in the leadership of District 13, she is pretty antagonistic against it; this changes several times in the novel. She decides to trust them and help them, but then she goes back to distrusting and disliking them. By the end, she wages a full-on war against that leadership, making some pretty powerful statements about power and control. So, her response to authority and leadership changes throughout the novel.
Secondly, we see her change quite a bit towards Peeta. For the first two books, she was unsure of her feelings for him; she was ambivalent and even took him for granted. However, him being taken away from her changes that quite a bit. She learns to appreciate all that he did for her. Her heart softens; she lets him in more. This softening of her character is interesting, because she is such a tough gal throughout most of the books. In this one, we finally see her letting Peeta in a bit, and actually softening.
Katniss' hard, outer shell also becomes a lot tougher in this novel. She deals with quite a bit of death and carnage, and on a much larger scale than she had to during the Hunger Games. She handles it quite well, stuffing her feelings and dismay about it deep down, and trooping onward. She hardens herself to death even more than she has in the past, and moves on to do what she knows she needs to. It gives her the capability to be more fierce, more decisive, and a better leader.
Along those lines, Katniss becomes a better leader in this novel. In the beginning, she was a social recluse, hiding out in corners of District 13, not wanting to be bothered or noticed. However, she changes through the novel; by the end, she is a determined leader, putting herself in the limelight over and over again, and confidently making decisions for her group. She matures quite a bit in that respect.
I hope those thoughts help; good luck!