Leia Organa is a princess, revolutionary leader, and trendsetter of the universe's most stylish Cinnabon-influenced hairdo. Although a princess of the Royal Family of Alderaan by birth, Leia served on the Imperial Senate before it was disbanded.
Leia's character exhibits an interesting duality. On the one hand, her role in the story is the classic damsel-in-distress; on the other hand, her character is a strong, independent woman who takes charge when necessary. Considering how badly Han and Luke bungled that prison escape, her leadership is necessary.
Damsel in Distress
Leia's role in the first half of the movie is to be the damsel in distress. True to the trope, she's kidnapped by a villainous villain and locked away in the Death Star, which is basically a space fortress. Unless you count the Dianoga (that's the worm-thingy) in the trash compactor, she isn't guarded by a dragon or monster… but her plight does move the heroes to action and unites them under a common cause. Alright, her money is what moves Han Solo into action, but we're counting it as part of the Leia package deal.
Leia joins a long tradition of distressed maidens going all the way back to tales of myth and chivalric romance. To name a few classic examples, we have: Brunhilde from the Icelandic and Germanic myth of Siegfried, the princess in the tale of Saint George and the Dragon, and the many abductions of Queen Guinevere in the Arthurian Legends.
Of course, the damsel in distress trope survived antiquity and lives in modern storytelling, too. We have Buttercup from The Princess Bride and Bella from Twilight . Disney made this trope its wheelhouse in its earlier animated efforts, and even video game yarns burst scared princesses, including the Nintendo's famous captive duo of Peach and Zelda.
Given that so much of Star Wars is drawn from mythology and classic story structure, it isn't surprising that Leia's role in the story should be the damsel in distress. With that said, she doesn't play it straight.
Gonna Hear Her Roar
To be fair, it is kind of difficult to be an independent woman when you're captured, locked up, and any means of retaliation are taken away from you. Yet Leia doesn't cower from the villain, nor does she pine for a hero to rescue her. Despite her damsel-y circumstances, Leia shows her strength of character and fights the Empire any way she can.
She stands up to both Darth Vader and Grand Moff Tarkin when facing them. Her willpower allows her to resist the mind probe and its menacing syringe. Even Tarkin's mention of her upcoming execution doesn't phase her poise; "I'm surprised you had the courage to take the responsibility yourself," she retorts.
However, the prime example of Leia's courage comes when Tarkin threatens to destroy her home planet, Alderaan:
TARKIN: Since you are reluctant to provide us with the location of the rebel base, I have chosen to test this station's destructive power on your home planet of Alderaan.
LEIA: No! Alderaan is peaceful. We have no weapons. You can't possible—
TARKIN: You would prefer another target? A military target? Then name the system. I grow tired of asking this, so it will be the last time. Where is the rebel base?
LEIA: Dantooine. They're on Dantooine.
Sure, her gambit doesn't pay off and Tarkin destroys Alderaan anyway. What's important is she lied to him knowing she would be caught. It isn't long before scout ships determine the Dantooine base has been deserted and Tarkin orders her to be terminated immediately.
Knowing this would happen, Leia was prepared to sacrifice herself to save her people. They were going to kill her anyway, but think of how much more painful and drawn out the Empire could have made her execution if she upset them. After all, look what Vader does to that Imperial commander who gets mouthy with him.
Completely at the Empire's mercy—or lack thereof—she still finds ways to fight and undermine its efforts. Unlike Han, she's not in it for the money, and unlike Luke, she isn't trying to fulfill a youthful urge for adventure. As far as we can tell, she's doing it simply because it is the moral thing to do.
… which makes Leia a boss.
Leia's Got a Gun
Step aside, Janie: Leia's got some shooting to do.
Once freed from her captivity, Leia's courage rackets up to eleven, and she takes the fight to the Empire. Despite Han's chagrin, she assumes leadership of the little group:
LEIA: Listen, I don't know who you are or where you came from, but from now on, you do as I tell you, okay?
HAN: Look, your worshipfulness, let's get one thing straight. I take orders from just one person—me.
LEIA: It's a wonder you're still alive.
She also fights alongside Luke. When they are cut off at the bridge, she takes Luke's gun and covers him while he prepares the grappling hook to swing them across.
Leia's role is minimized during the movie's climax as the focus shifts to Luke's struggles during the Death Star assault, but Leia's position in the command center makes it clear she has embraced her role as a Rebel leader.