Princess Leia Organa is a primary character in the Star Wars continuum. The twin sister of Luke Skywalker and daughter of Anakin Skywalker and Padmé Amidala, she is a stubborn, argumentative woman who eventually becomes a Jedi Knight and marries the smuggler Han Solo. In the films she was played by Carrie Fisher.
In canon, she is a sensible, mature young woman—mature enough to be in politics at the age of twenty, and brave enough to support the Rebel Alliance to the point of being a key figure. She is not initially amused or wowed by Han Solo's attempts at humor and is a serious, but kind person. Amazingly, throughout the entire classic trilogy of movies, Princess Leia almost never misses a blaster shot outside of a large "everybody is shooting" scene.
She is not featured as much in badfic as her brother or father, but more than Han Solo. Often she is the subject of badly implemented AUs where Darth Vader/Anakin Skywalker figures out that she is his daughter earlier than in canon, or even stories where she is raised as the daughter of (an often suitless and uninjured) Darth Vader from birth. Sometimes she is portrayed as selfish or petty. Or, in the case of the aforementioned fic genre, she may appear as a full-blown dark Jedi or Sith... yet trust her to be the speshul good Sith that turns her father good again and kills that nasty old Palpatine.