****Spoiler Alert, if you haven't seen the original Star Wars trilogy, in which case shame on you****
Han may have a bit of an unfair advantage here, I will admit, and not only the advantage of being played by Harrison Ford.
So while Luke's having his heroic journey, training to master his Jedi powers, confronting his evil dad, causing a massive galactic power vacuum with the power of goodness, all that classic stuff that at least one major hero needs to do every generation but that manages to suck most of the considerable natural charisma out of Mark Hamill, Han gets the advantage of being badass sidekick and romantic lead rolled into one, the interesting parts of being the hero without the drag.
If you haven't seen it, well, refer to my spoiler alert above. But here's a refresher anyway.
Han is a smuggler who travels the galaxy with his Wookie friend/bodyguard, Chewbacca.
And yes, that is how this scene went.
Luke hires Han to fly him to rescue Princess Leia, and Han accepts under the promise of lots of money and an excuse for an excursion into the territory of a bigger bad guy than the Hutts where he's unlikely to be followed.
Han does the job effectively if haphazardly, but when Han and Leia actually meet, things explode into sexual tension bickering. She's a high-ranking diplomat and rebel, used to being in charge and having everything go according to plan, and she's having a very bad day, what with her home world getting exploded before her eyes. Han's irritated by every one of these qualities and especially the fact that he's starting to like her anyway.
Lando double-crosses them (under blackmail), Han gets frozen in carbonite for transportation back to Jabba the Hutt, and when Leia confesses her love right before he goes into the freezer, he opts for roguish over sappy.
We've got an outlaw with all the danger and on-his-toes improvisation, charisma and guts we love to associate with the word, who can actually sell Lucas-style romantic dialogue.
And unlike the vast majority of heroes of believably morally ambiguous background, he's got a good heart that actually wins out in the end, rather than hovering forever out of reach behind his ambiguity. This is a guy who goes from smuggler running from and killing mob bounty hunters to two-time hero and General of the Rebel Alliance. That's a bigger arc than our actual hero.
And now, just for the fun of it, Han jumping into the task at hand half-cocked but full-assed, as you’d hope an improvising roguish outlaw would when cornered.