In reference to this question about if Obi-wan become more powerful, I'm curious to know how it was possible for him to become more powerful.
In reference to this quote:
You can't win, Darth. If you strike me down, I shall become more powerful than you could possibly imagine.
Just after this Darth Vader swings at Obi-wan and just prior to being sliced cleanly in half Obi-wan dissipates, and as such he remains unstruck.
Would Obi-wan have been more powerful if he got Darth Mauled in twain?
The answer to this goes back to Qui-Gon Jinn, who was Obi Wan's master and the philosophy they both shared.
The Background
Both Qui-Gon Jinn and Obi Wan Kenobi were proponents of The Living Force. The Living force was a view on the force that was one of the two major scholarly schools of thought within the Jedi Order. The other, albeit less popular, being The Unifying Force. Wookieepedia does an excellent job of explaining the basics of the philosophy:
The Living Force was thought to be present in most living beings, surrounding and penetrating them, thus making all living things connected by it. The Jedi believed the Living Force relied on their instincts and were attuned to other living beings around them. They were mindful of the future and the possible consequences of their actions, but remained focused on the present.
Being focused on the present was a huge part of Qui-Gon's general attitude. Qui-Gon also uncovered a very powerful secret within the Living force, which was the ability to turn into a Force Ghost. This was a seemingly immortal preservation of a Living Force adherents consciousness. He was not the first to do this, but he was the first in recent history to express knowledge of the ability.
Obi-Wan's Statement
You can't win, Darth. If you strike me down, I shall become more powerful than you could possibly imagine.
The ultimate goal of almost every single Sith, since the force wars, has been the ability to cheat death. Some succeeded with their own methods, such as Emperor Vitiate or Darth Sion, but none of them were fool proof. This is where the concept of a Force Ghost comes in. To become a Force Ghost, one must convert all of their matter into pure force energy. They remain tethered to this realm, but as non-physical entities. They also appeared to gain an increased awareness.
Examples of his Power
For example, when Yoda fails to defeat Darth Sidious, he places himself into exile on Dagobah. He only appears to tell his driver, Bail Organa. Yet in the films, Obi-Wan seems fully aware of Yoda's whereabouts.
Another is Obi-Wan's ability to appear, at will, to Luke Skywalker during points of turmoil to offer guidance. This seems to imply that Obi-Wan now has the ability to traverse space at will, given that he still exists in the physical realm (albeit as a non-physical entity).
Finally, the big one. He is immortal. As a Jedi, he has a moral duty to give himself up and become one with the force when his work is done, but he does not have the same requirement that the rest of us has. In short, he can choose when to die.
Confrontation with Darth Maul
During the battle with Darth Maul, Qui-Gon had already uncovered and mastered the art of becoming a Force Ghost, however Obi-Wan had not. Qui-Gon had shared his knowledge of the art with Yoda and Obi-wan posthumously. If Obi-Wan had died during the fight, he would have become one with the force.
He didn't disappear before he got hit, he was killed by Vader and became a Force-ghost. It simply looks like he disappeared before being struck due to special effects limitations in 1977. Such Force-abilities were as-yet unknown when Darth Maul was killed.
