What happens in Mockingjay?

A lot happens. The big deal in the story is that the Rebels begin to use Katniss to get supporters for their cause. They put a bunch of makeup on her, put her in an outfit she finds out that was designed by Cinna and take her to different war zones to get footage to make propaganda commercials.

She isn't too happy about this but plays along, thinking that maybe she's going to get to fight finally. But she eventually realizes that District 13 is playing her just the same way that the Capitol did.

Eventually she agrees to be their 'Mockingjay' (a symbol of rebellion) if Prim get to keep buttercup (her cat) and if they will rescue Peeta for her. They do, but by the time she gets him back he has been driven crazy and made to think terrible things about Katniss, to the point that he gets violent every time he's around her.

So things progress, and after a lot of training she convinces them to let her go into the capitol. Peeta and Finnick go with her, and a few others. It's supposed to be a propaganda thing, more war movies, but their leader dies (Boggs) and Katniss ends up being put in charge.

At some point Finnick dies, too by lizard mutts. They keep moving on. Peeta isn't violent towards Katniss anymore but he's not sure how he feels about her. They start playing a game called 'real or not real' to help him decide whats true or not. For example, Katniss is a mutt = not real. They eventually get to the outside of President Snow's mansion. Katniss of course has every intention of killing him.
They find then that a bunch of children are being held outside the mansion and a bunch of medics are dropped in to help the injured.Katniss sees that one of the medics is her sister. Before she can do or say anything a parachute bombs are dropped and Prim dies.

When Katniss wakes up, she's in the mansion. She is told that they have won the war and she is going to symbolically execute Snow with one of her arrows. But she doesn't feel that is right.

She has a conversation with Snow in which she realizes that the President of the rebellion is just as bad as he is and, on top of that, is the one who ordered the bomb to be dropped that would kill Prim
As Katniss goes out to execute snow, she realizes how alike she and Haymitch are because she has decided what she will do. As she strings her arrow she doesn't strike Snow; instead, she shoots the new President (Coin)and kills her immediately.

She learns that her mother will stay in the Capitol and Gale will not be returning home either. Only she and Haymitch go back home. 

Katniss is severely depressed for a while. Then one day somebody arrives outside her door. It is Peeta. They begin a slow friendship, Peeta now over the effect of what the capitol did to him. The friendship becomes love, and eventually they make love. Peeta asks, "You love me. Real, or not real?" Katniss responds, "Real."

There is then a brief epilogue where it is revealed that after fifteen years Katniss and Peeta have two children, a boy and a girl. She reflects on the fact that her children play on a grassy field that they do not know contains hundreds of bodies. That's the end!

This is a very short version!