So first of all, if you're at all afraid of spoilers about the show, don't read any more of this.
Seriously, I'm going to talk about how the show ended.
Okay.
So there's two sides to this. One is the nature of the setting. The other is how the players fit into things.
Setting
Ultimately the whole setting of LOST comes down to five key elements. I needed to make sure I had a clear understanding of the mysteries so I wouldn't be making stuff up as I went along. Some things I changed from the show or made up myself so it made sense to me.
First, the island is a magical place in a world where magic is rare. Occasionally the island moves, time flows oddly there relative to the outside world, and some people well attuned to the island can heal miraculously. These and other oddities are due to a strange glowing power source in a cave at the 'heart' of the island.
I have decided how the magic works, in case you're interested.
[sblock]I'd just read the novel Anathem, which examined the concept of alternate realities. Every time anything happens, even random fluctuations at the quantum level, multiple possible worlds are born. Most fritter away and don't form their own unique timeline branch, but occasionally discrete realities fork and endure.
Master monks could consciously choose which branching path they would move into. And the most skilled of all could choose to skip sideways into alternate worlds before they frittered away. This let them be effectively ageless, since they could choose whether their cells had errors in replicating, and they could avoid getting injured by simply picking a reality where they'd moved slightly differently.
So in my LOST, the island is basically a source of quantum flux, and people on the island can sometimes just tune into it and make weird stuff happen, while those who've been there long enough can straight-up do magic. The 'heart' of the island is just where the flux is centered, and the energy from it is carried throughout the island by streams, some of which are subterranean.
I felt this tied in nicely with Desmond's visions of possible futures, and the whole flash sideways stuff (which in the show ultimately made me guffaw when they revealed what it was).[/sblock]
Second, the island has a guardian who lives a long time but isn't unkillable. A long long time time ago the then-guardian had two possible successors, whom she raised as her sons. One brother, Samuel, was curious and had a natural affinity to the island's power, but he got upset that 'mom' kept secrets and wouldn't let them leave the island. The other brother, Jacob, was more loyal to his mom, but not as magically gifted. They would fight as children, so their mother magically proclaimed that neither would be able to harm the other.
When a group of ancient Roman castaways got stranded on the island, Samuel went to join them. He tried to build a boat to leave the island, but his mother killed the other castaways to stop him. In retaliation, Samuel killed his mother. Jacob was enraged but unable to harm his brother, so he threw him into the cave that was the heart of the island. The energy of the cave would have destroyed Samuel's body, but because he was so closely attuned to the island, he was able to survive as a semi-tangible being of black smoke. He can also take the form of dead people, read people's minds, and make really creepy sounds in the woods.
Third, Jacob is the current guardian of the island. He and Smokey have a long feud, but since neither can directly harm the other, Jacob keeps his brother trapped here. Indeed, Jacob's limited magical prowess was for a long time enough to keep anyone from leaving the island, because he fears if others found it they would destroy or exploit the heart. He thinks if the heart dies, the world dies.
Smokey, meanwhile, tries to trick those who few people who find the island, and makes them try to kill Jacob. Apparently over the past two thousand years a few cycles of this have played out, with Jacob often getting the upper hand and sealing his brother away. Tiny cultures rose and fell, leaving strange ruins from different eras scattered across the island.
Fourth, in the 19th century, a slave ship (owned by Magnus Hanso; more on him in a minute) crashed on the island. Smokey tried to get the survivors to kill Jacob, and in the end everyone on the ship died except for one former slave, Richard, who helped Jacob trap Smokey in one of the ruins on the island. Jacob, having grown weary of human contact, made Richard immortal in exchange for his help; he didn't think Richard had quite the right demeanor to be the island's guardian, he tasked Richard with helping him find a replacement.
Jacob started to guide ships to the island, but he never managed to find someone he thought would be faithful to the island. The people who remained (which we'll call "the Others") came to revere Jacob, but they only knew of him through Richard.
Now, as for Magnus Hanso, there was one way to leave the island: a buried mechanism Samuel had designed before he became Smokey. Operating it would displace the island, and deposit the person who used it in one of a handful of locations around the world. Magnus was an earlier castaway on the island, but with Smokey's help he had been able to get free. He was supposed to send to the island scoundrels, who would kill Jacob, but the ploy failed.
Fifth, in the 1970s the island was discovered by a group of scientists and researchers known as The Dharma Initiative, founded by Alvar Hanso, descendant of Magnus, who used his great-grandfather's tales of a magical island as a guide for his own exploration. Unfortunately the leader of the first expedition, named Horace, accidentally released Smokey. Smokey then managed to mislead the Others and trap Jacob in a seaside cliff cave from which it was impossible to escape.
Richard suddenly could not find Jacob, and he lacked any power himself to drive off the Dharma Initiative, so he arranged a compromise, wherein he hoped to keep the Dharma folks from endangering the island. Dharma stuck mostly to the shore of the island, but they built all manner of scientific research stations to try to understand and harness the unusual energy on the island. With Jacob away from his seat of power, his control of the island was weaker, so Dharma was able to come and go through a few carefully-navigated paths.
It wasn't until later that Richard realized that Smokey was free and trying to tempt his people. Blaming Dharma, he arranged a plot that turned Dharma's own technology against them. With the aid of a few people on the inside, Richard and the Others massacred the Dharma Initiative. Most of Dharma's facilities fell into disrepair, but the handful of DI members who sided with them helped the Others make use of a few stations. Richard kept up the charade that Jacob was calling the shots, and told the Others that it was up to them now to protect the island.
So that's the setting in a nutshell.