Character Analysis
Obi-Wan: the uncle we all wish we had. He's cool, drily hilarious, and more than willing to teach the fine art of lightsaber-ing and Force-mastery. Oh yeah: and he can also manipulate the minds of pretty much anyone he wants to.
Obi-Wan Kenobi was once a master in the order of the Jedi Knights where he fought in the Clone Wars. After the Jedi were hunted to near extinction by Darth Vader, he went into hiding for twenty years, living in the boondocks of a secluded desert planet. He comes out of hiding to teach young Luke Skywalker the ways of the Force—only to be killed.
This guy has had a rough life, but since he's another in a long line of the old mentor-type characters, that's to be expected.
Old Man, Look at My Life
Obi-Wan is perhaps the best known of the old mentor type characters, although he's far from the original.
The archetype goes all the way back to Merlin from the Arthurian Legends but also includes Gandalf from The Lord of the Rings, Dumbledore from the Harry Potter series, and Ged in the later Earthsea novels.
Broadly speaking, these characters are old men who teach young heroes about their powers and push them toward the quest they will have to undertake to complete their destinies. Old man mentors have special powers they use to help the hero, and sometimes they pass these powers on. They ultimately die before the hero can complete the quest, forcing the hero to face his final challenge on his own. Typically—but not always—they live in nature. They also sport amazing thinking beards… all that thinking they do must help the beards grow.
As you can see, Obi-Wan passes the old man mentor test like a pro. He lives as a hermit in the Dune Seas before being pulled out of retirement by Luke. He gives Luke a lightsaber, teaches him the ways of the Force, and sets him on the path to his destiny. Finally, Obi-Wan perishes at the hands of Darth Vader, leaving Luke to continue on his own.
Oh yeah: his beard is just glorious.
The Force 101
Obi-Wan's main task in Star Wars is to teach Luke about the Force. He doesn't get much time to teach his young padawan, but he makes use of the time he has. First he instructs Luke as to what the Force is:
"The Force is what gives a Jedi his power. It's an energy field created by all living things. It surrounds us, penetrates us, it binds the galaxy together."
Later, he instructs Luke on how to actually use it:
OBI-WAN: Remember, a Jedi can feel the Force flowing through him.
LUKE: You mean it controls your actions?
OBI-WAN: Partially, but it also obeys your commands.
[…]
OBI-WAN: I suggest you try it again, Luke. This time, let go your conscious self and act on instinct.
Obi-Wan's not around long enough to impart all the info there is about the Force, but we can see that it does reach Luke. During the film's final battle in the Death Star trench, Luke remembers Obi-Wan's words and trusts the Force. Whether Luke is simply remembering Obi-Wan's teachings or Obi-Wan is communicating beyond the grave is a little ambiguous in this film, but either way, it shows that Luke is using what Obi-Wan taught him. This allows Luke to destroy the Death Star and save the day.
As a result of Obi-Wan's teachings, Luke is able to set out on the path toward his destiny of becoming a Jedi Knight.
Sacrifice
Ultimately, Obi-Wan is defeated at the business end of Darth Vader's lightsaber. Well, defeated is probably a bit strong. As he tells Vader:
VADER: Your powers are weak, old man.
OBI-WAN: You can't win, Darth. If you strike me down, I shall become more powerful than you can possibly imagine.
VADER: You should not have come back.
At the conclusion of their fateful duel, Obi-Wan lifts his lightsaber in a stance of submission and lets Vader strike him down. Whether his increase in power is Luke taking his place or his ability to communicate after death (both?) is left ambiguous.
James F. Iaccino notes the importance of this sacrificial act. He states,
Old hermit Ben knew that as long as he was physically present, the boy would never develop on his own or embrace the ways of the Force. Ben's sacrifice was, therefore, a necessary one to help Luke find himself (and his destiny).
As long as Luke continued to rely on Obi-Wan, he would never be able to fully embrace his path to being a Jedi. Knowing this, Obi-Wan trained Luke with the knowledge he would need in a Jedi crash course and accepted his death. Like many old man mentors before him, Obi-Wan chooses to perish so that his student might succeed.