The Mockingjay, in the novel Mockingjay (of The Hunger Games trilogy) symbolizes many different things.
Katniss' first real brush with the Mockingjay happens in novel one. She receives a pin with the mockingjay on it from the mayor’s daughter, Madge Undersee. Also during her first appearance in the Hunger Games, Katniss befriends a young tribute from District 11, Rue. Rue reminds Kantiss of her sister (Prim) and they create a way to talk back and forth during the games using bird calls.
As the novels move on, Katniss comes to know that the mockingjay came about after a bad decision of the Capitol's. (The Capitol created the jabberjay, they escaped from the Capitol, and mated with mockingbirds.) Katniss is, therefore, symbolic of the mockingjay herself. She is, ultimately, a creation of the Capitol after her trip to the Hunger Games. She was changed and became something completely different than what she was prior to the games.
For the final novel, the mockingjay represents the rebellion against the Capitol. Katniss, being the perfect symbol to represent the rebellion given her dislike for the Capitol, becomes the Mockingjay.