Here's the #1 shocker of The Phantom Menace: although it stars Liam Neeson, Liam Neeson isn't seeking revenge on anyone. No one stole his daughter. No one is harming his family.
Yup: Liam "Vengeance" Neeson is a peaceful Jedi knight of the Old Republic. And that means keeping a zen-like calm at all times. This is as weird as seeing Seth Rogan play a grizzled mafia don, or Daniel Day Lewis play a campy comedic sidekick.
But back to the show:
As a respected and trusted Jedi, Qui-Gon Jinn is sent by Chancellor Valorum to serve as an ambassador to negotiate an end to the Trade Federation's blockade of the planet Naboo. Yawn? Not so much. This event leads Qui-Gon to take the lead in an adventure that will uncover a mysterious dark force lurking in the galaxy. (Dum dum dumm.)
He's an interesting character in that he takes the DNA of two archetypes—the young protagonist and the wise old mentor—and splices them together. In this way, he proves a hybrid of Luke Skywalker and Obi-Wan Kenobi from A New Hope—he's both the protagonist of the adventure and the one training the next generation to take up the cause.
Qui-Gon isn't, say, a restless youth from a village recently burned down by marauding evildoers, so it isn't immediately obvious that he's the protagonist.
He has very little at stake during the first act, since it isn't his home planet being invaded. And although he helps Queen Amidala and her court, it has more to do with the Code of the Jedi requiring it and—let's be honest—because he needs a ship to get off Naboo.
But he's the protagonist of this adventure all the same: he's the character we root for and the one we hope will succeed in the end. As the story progresses, the stakes get higher for him. He finds Anakin Skywalker and believes him to be the chosen one, a Jedi predicted by prophecy that would bring balance to the Force. And after confronting Darth Maul, Qui-Gon realizes the Sith have returned to the galaxy.
Both give Qui-Gon something to fight for. We want him to root out the Sith, defeat them, and bring peace to the galaxy. We also want him to train Anakin so the boy can grow to meet the better half of his destiny.
But even though Qui-Gon is the protagonist, he isn't invincible, lacking a shiny set of plot armor. During his second duel with Darth Maul, Qui-Gon is slain, and although Obi-Wan manages to defeat the Sith, it's too late for the older Jedi:
QUI-GON: [Muttering] No, it—it's too late.
QUI-GON: Obi-Wan. Promise—Promise me you'll train the boy.
OBI-WAN: Yes, Master.
QUI-GON: He is the chosen one. He will bring balance. Train him.
As the next generation of heroes, Obi-Wan takes up his master's causes, but this being prequel territory, we know neither will ultimately succeed: lil' Anakin is destined to become Mr. Darth Vader himself.
With Darth Maul dead, the Sith lord Darth Sidious is able to slink into hiding, and we know that Anakin is doomed to become Darth Vader. Despite knowing the inevitable, we still root for Qui-Gon and his causes… no matter how many times we watch the film. (We always cry when he dies, too.)
He Will Find You
And he will teach you. In addition to protagonist duties, Qui-Gon also serves as the film's mentor archetype. Even his appearance clues us in to his teacher role— his beard and long hair are shout-outs to the old master trope (Gandalf, anyone?), and his fashion sense is similar to Obi-Wan Kenobi's from A New Hope—even if old Obi-Wan kept his top trim.
Qui-Gon taking on the Obi-Wan role is a little ironic here because he proves that he's an inferior Obi-Wan… than Obi-Wan. He's just not as Force-savvy. We see this from the first interactions between the two:
OBI-WAN: I have a bad feeling about this.
QUI-GON: I don't sense anything.
OBI-WAN: It's not about the mission, Master. It's something… elsewhere, elusive.
QUI-GON: Don't center on your anxieties, Obi-Wan. Keep your concentration here and now, where it belongs.
OBI-WAN: But Master Yoda said I should be mindful of the future.
QUI-GON: But not at the expense of the moment. Be mindful of the living Force, young Padawan.
OBI-WAN: Yes, Master.
Even on a mission to serve as ambassadors, Qui-Gon uses the opportunity to teach his young Padawan about the Force—specifically his philosophy of the Force.
Long Live the Living Force
Qui-Gon believes in a "living Force." This means focusing on the moment and trusting the Force to guide you rather than overthinking or worrying about proper action. (Yeah. This sounds like a really nice mindfulness exercise if you want to, say, decompress from your commute… but it ain't a great way to ward of the Sith.)
But taking the "living Force" route isn't always useless. Qui-Gon trusts the Force to guide them through the Naboo planet core in lieu of his useless navigator. He also believes in Anakin's podracing plan… despite it having more moving parts than a Rube Goldberg machine.
Qui-Gon takes on a second, unofficial apprentice, Anakin Skywalker. We see him begin to teach Anakin before the podrace when Qui-Gon tells the boy, "Remember, concentrate on the moment. Feel, don't think. Use your instincts."
Although different words, the lesson is the same as the one he taught Obi-Wan: believe in the living Force and let it guide you through intuition, not reason.
The Jedi knight attempts to take Anakin as his Padawan, but the Jedi council refuses, saying he's too old at the ripe age of ten or twelve. Despite this, Qui-Gon teaches the boy unofficially:
QUI-GON: I'm not allowed to train you, so I want you to watch me and be mindful. Always remember: Your focus determines your reality."
And this brings us to—
Rebel with a Cause
Qui-Gon is wise and courageous, but he also has a defiant streak in him. In this way, his character plays against the mentor role—we typically associate rebellion with youthful characters rather than venerable moldy oldies.
This Jedi knight is particularly defiant against authority. When Panaka initially asks Qui-Gon to take Padmé into Mos Espa, Qui-Gon calmly responds, "No more commands from Her Highness today, Captain," as though saying no to elected royalty is commonplace.
This is further shown when Padmé tells him the queen would not approve of his plan, and Qui-Gon says, "The queen doesn't need to know." This hints that Qui-Gon knew Padmé was the queen the whole time. Just look at that smile when Padmé reveals herself to Boss Nass; Qui-Gon was in the know, y'all.
But his dislike of authority is most obvious when it comes to the Jedi Council. The way Mace Windu discusses matters with Qui-Gon—eyes rolling, exasperated voice—suggests his defiance is an ongoing issue, and Obi-Wan flat-out says Qui-Gon would be a Jedi master if he could only learn to get along.
But Qui-Gon's defiance is most prevalent in the following scene:
MACE WINDU: No. He will not be trained.
MACE WINDU: He is too old.
QUI-GON: He is the chosen one. You must see it.
YODA: Mmm. Clouded the boy's future is.
QUI-GON: I will train him then. I take Anakin as my Padawan learner.
YODA: An apprentice you have, Qui-Gon. Impossible to take on a second.
MACE WINDU: The code forbids it.
Qui-Gon doesn't give two hoots for the code or for the authority of the Jedi Masters. Just like with Padmé, he will do what he thinks is right and necessary… regardless of the decisions or reasoning of others.
And this turns out to be a truly terrible stance to take.
Star Wars: The Next Generation
Despite not appearing in any other Star Wars film, Qui-Gon's influence on the saga can be felt through his students, Obi-Wan and Anakin.
Obi-Wan inherits some of Qui-Gon's defiance—as evident by his request to train Anakin—but he mostly embodies Qui-Gon's sage-like qualities. This is especially prevalent in the original trilogy when Obi-Wan repackages and repurposes many of Qui-Gon's lessons for Luke Skywalker.
He tells Luke to "let go of his conscious self and act on instinct" during their training session on the Millennium Falcon and even drops Qui-Gon's "truth from a certain point of view" line on him in Return of the Jedi.
Anakin, on the other hand, exhibits Qui-Gon's more rebellious qualities. He's often frustrated with Obi-Wan's teachings and the decisions made by the Jedi Council. In Attack of the Clones, Anakin marries Padmé despite the code forbidding it… because he believes it's the right thing to do (read: he lurves her) and that the code is incorrect.
In the end, Qui-Gon's goal of bringing balance to the Force is achieved… though it takes yet another generation in the form of Luke Skywalker to achieve that goal. Or does it? The newer episodes muddy even that point…