On the Island is a river. This river runs from its source in high ground (one of the large hills), down into a valley, and then into an underground cave. There it cascades over a waterfall, and builds up into a pool, the Source Pool. Here it mixes with The Light, and flows out towards the sea through an underground river. As it flows out to sea, it mixes with sea water and dissipates across the world, into the clouds, and into all the water of the world, eventually passing into the bodies of all people and animals.
The Light is the currency of time. Although light in general is a wave, The Light is a fluorescent particle, which dissolves in water. The Light allows all events to occur. It is time itself. The particles of The Light do not have a fixed time and space. This is their power, that they can slide backwards and forwards without a linear progression. Without The Light, time stops and nothing can live, or die. It has incredible high electromagnetic properties, which cause people and animals in close proximity to become unhinged in time, in high enough doses. As the Mother says to Jacob and MiB, it brings life and death. The Source Pool in the cave is where all The Light in the world comes from, and thus is the source of time.
When the water leaves the Source Pool, it travels through a river to the coast, under various parts of the Island. Many of these places were located by the various inhabitants of the Island including The Others, Jacob and his brothers people and Dharma. These include The Swan Hatch, The Orchid and the various wells. At these locations, the electromagnetism is at a relatively safe level compared with the Source Pool, and experiments can take place. The sea around the island has an abnormally high amount of The Light in it. This is why there is a time delay when Faraday sends his rocket from the Freighter to the Beach.
At some point, the Man in Black (MiB) discovered if he altered the flow of the river he could unhinge the Island in time. He created the wheel under the future site of The Orchid, and created a series of locks to dam the water and redirect it. The wheel controlled this movement.
When the stream is blocked, The Light is contained inside the Island. This means the rest of the world stops moving through time (something that the rest of the world would not experience, you could only view it if you were on the Island). The Island, however, would keep progressing.
The detonation of Jughead in 1977 was always meant to happen. This is why The Swan exists in the first place, and the remains of it still exist when the Losties are send back to the Present (which occurs due to their exposure to a very high concentration of The Light). The bomb caused the underground river to be revealed. This means a high concentration of The Light would be released all the time, which would be dangerous. The Swan hatch is the nearest known source to the Source Pool. This is known because the bamboo forest is close to the beach (as its where Jack woke up), and the Swan is fairly close also (close enough for John and Boone to get from there back to the beach quite quickly).
The Dharma initiative could have just plugged the breach, but they wanted to experiment on it, due to it's concentrated nature (far more concentrated than The Orchid). They put scientists into the Swan, and quarantined them in, telling them that the air was poisoned. After the Purge, the Swan scientists carried on without the knowledge of the purge, as they were locked inside. The supply drops are drops sent using The Orchid. Using the power of The Light, during a lockdown event, a message is sent back in time to the 1970s Orchid, who send a supply drop forward in time to the source of the message.
Every 108 minutes the button must be pressed to diffuse the build up of The Light and allow the river to carry on running. The failsafe detonates via implosion the mechanism Dharma set up for the experiments, removing the danger but destroying The Swan. It was put there just in case the experiments got out of control. When Oceanic flight 815 flew overhead during event, The Light seeped upwards as electromagnetic waves which ripped the plane apart, causing the crash. The same light also brought the survivors down to the ground in a fairly safe manner, explaining why so many people survived a pretty horrific plane crash. A similar thing happened when Juliet was pulled down into the Swan construction site in the 1970s, which is why she survived.
When Ben turned the wheel, he knocked it off axis. This meant the The Light was still moving out from the Island, but inconsistently. The Island jumped through time, as it's relative position with the rest of the world was in constant flux. When Locke moved the wheel, it restored the flow, but being in close proximity to The Light (which happens during the turning) moved him in spacetime (to Tunisia).
The sickness is caused by people drinking the water downstream from the Source Pool. This water has a high concentration of The Light, and can cause people to become unhinged from time and, from their point of view, reality, causing insanity.
At exactly the right concentration, drinking The Light can make you have supernatural powers. These include the ability to accelerate and control healing (Jacobs touching Locke helped repair a lot of the damage of his fall) and the ability to stop the visible effects of aging. When a Guardian (Mother, Jacob, Jack) pass on the torch to the next Guardian, they drink from a part of the stream very nearby to the Source Pool. In this water is the correct concentration of The Light required. The touch of the previous Guardian seals the deal, and grants you the same power (which lasts forever, or at least until all of The Light has left your body).
If The Light goes out (it stops being mixed with the river in the Source Pool), time in the outside world slows down to a halt (once all of the current Light has been used up). However, because all the particles are connected, extinguishing The Light also means that The Guardian will lose his or her powers, making them mortal.
When Desmond removed the stone and the water stopped mixing with The Light, the Island started to sink. This is because the Island is a separate entity from the Earths crust - the only way which it can move (if it was a joined entity, it wouldn't be able to move independently). It stays afloat because it is constantly moving.
When the stone is removed, there is still some Light left in the water around the cave. This is why Jack was able to pass his powers on to Hurley. When all the Light is used up, the island sinks.
Because Kate kills MiB, all the events leading up to her doing that have to happen. Therefore, for the continuation of The Light, all of the people who effected her and caused her to walk that path on the Island must live. These are the names of the candidates that Jacob found. They are the people who collectively will kill the evil on the Island.
Because he knows this, Jacob allows the candidates to chose. They can be the Guardian if they like, it doesn't matter who does it, as he knows together they will win his war against his brother. This is how Jacob won.
Anyone who is a Guardian, or who helps in guarding The Light moves upon death to a parallel universe which exists as if The Light had gone out, and they never had contact with the Island, or the previous Guardian (in this case, Jacob). This flash sideways universe is slowly dying as The Light is not being replaced. As more and more of the candidates die, they all move into the universe. When Jack dies, he moves into that universe too. You can stay there as long as you like with the people you love. Christian is the first to move on, as he is from the previous generation and already has made peace with the world. One by one, the candidates will pass over into The Light, and be absorbed into it.
When you die, you go to a place, and that place can last for a nano-second or can be an extended period of time, where you have to remember your own death and all of the people that were instrumental, that you loved the most and helped you the most, and were the most important to you, you have to remember all of them and remembering them lead up to the moment that you died before you can move on.
After Jack’s death, Hurley and Ben continue to run the island, and look after it for many centuries, until Hurley uses the same foresight as Jacob to create a new list of candidates who will protect the island from evil. He allows people to come and go from the island, something which Jacob never allowed. When eventually Hurley and Ben die, all of the candidates are now in the sideways timeline, and their memories begin to be awoken. Because the timeline is unhinged in time, they all start the timeline at the time they first arrived on the Island (September 22nd 2004), but all leave the main timeline at different times (their deaths). The older characters (the Witmores etc) who came to the Island much earlier return to THAT time instead of September 22nd. I also assume that Richard Alpert moved to the FST, but he moved back to the 18th century.
Desmond as the only one aware of purgatory on the island makes sense due to his "specialness." Speaking of which, with the many characters who, rightly or wrongly, were called "special" throughout the series, Desmond was probably the one who deserved that title the most.
All of Desmond’s ‘episodes’ (when he turned the failsafe etc) are his brain moving to the FST. When Desmond goes back to buying the ring, Eloise is the only one in the FST universe with memories of the main timeline (as the time she arrived on the Island a long time before the current Losties), which is why she is his ‘guide’ during his first jump - she knows what is going to happen as she has lived through it.
Eloise tried to stop Desmond from making the Losties remember, because she wanted to keep Faraday in the FST as her wanting to live in a reality where she never killed her son. Thats also why she asked Desmond if he is going to take him too. But he replied "not with me". And in a way, it's true, but it's also a little sad for Faraday, Ana Lucia and others (Walt?) who haven't fully remembered, or aren't ready to, "let go."
Mostly written by some guy from The Fuselage, but some parts at the end are added and written by Zeratul (me).