The island is a mystical place where the struggle between good and evil has been played out for centuries. The trials that the Oceanic survivors went through on the island created a strong bond between them and pushed them into becoming better people. Some people died on the island while others left and lived long lives afterward. Because of the bond between them, the Losties' collective consciousness created a sort of after-life waiting room where their souls gathered following their respective deaths. They waited there until Jack arrived so that they could all move on together.
The island contains a mystical glowing yellow light that pours out from deep inside. It is said that this light is "life, death, rebirth, everything". An apparently god-like man named Jacob has spent centuries protecting that light from his twin brother (who is never named in the series but is referred to by fans as MIB since his first appearance was as a man dressed in black). In a fit of rage, Jacob killed MIB and threw his body into the cave from which the light emanates. This action created (or released) the smoke monster, which can assume the physical form of people who have died.
MIB wants to leave the island but is bound to it by Jacob. Jacob and MIB cannot kill each other.
Jacob and MIB disagree about whether people are basically good. The people who come to the island over the centuries are viewed as pawns in this conflict.
The Others are people on the island who have come to follow Jacob in an almost religious manner. Richard Alpert, Jacob's liaison to the Others, has been made ageless by Jacob in return for his service. Richard came to the island in 1867 aboard the Black Rock (the slave ship that was found wrecked in the middle of the island).
The mysterious whispers are the sounds of dead people who are trapped on the island and can't move on.
The broken statue on the island was a rendering of Tawaret, the Egyptian goddess of protection, birth and fertility.
In the 1970's, a group called the Dharma Initiative built several structures on the island (as well as on the nearby Hydra Island) in order to study the island's unique properties which include extremely large pockets of electromagnetic energy. The polar bears were brought to the island as part of their experiments. In 1977, a disastrous event referred to as "The Incident" occurred. This led the Dharma members to build a computer-controlled system designed to safely release built-up electromagnetic energy. In order to do this, the numbers 4 8 15 16 23 and 42 (Hurley's cursed lottery numbers) had to be input into the computer every 108 minutes.
Benjamin Linus, the son of one of the Dharma workers, joined the Others and took part in a massacre of the Dharma members. The Others then took over using the Dharma facilities for their own purposes.
In 2004, Desmond Hume (who was shipwrecked on the island during a yacht race) failed to input the numbers into the computer on-time and the resulting burst of electro-magnetic energy caused the crash of Oceanic Flight 815.
A wheel in an underground chamber on the island (similar to an earlier device that MIB's people believed would harness the light's power) can be turned to make the island move in time and space.
Through a series of events, some of the Oceanic survivors find themselves on the island in the year 1977. They come up with a plan to prevent their plane from crashing by using a bomb to blow-up the pocket of energy which triggered the crash. Their plan actually creates "The Incident" and sets off the events that led up to their plane crashing.
The explosion during "The Incident" appears to have created a split in time. In one world, the Oceanic people on the island have moved from 1977 back to the present. In the other, the audience is shown a reality in which the island has sunk and Flight 815 arrives safely in Los Angeles. None of the people on board the plane appear to have any memories of what happened on the island yet they seem to feel a connection any time they encounter another 815 survivor in their daily life.
Jack, Sawyer, Hurley, Kate, Sayid, Locke and one of the Kwons (which one is never indicated) were destined to come to the island because Jacob believed they were candidates to replace him as the island's protector. Jack eventually accepts the responsibility.
MIB tricks Benjamin Linus into killing Jacob. He plans to break free of the island by killing off all of the 'candidates'. He later decides to extinguish the mystical light and sink the island. He succeeds in putting out the light but the act makes him mortal, allowing Kate to shoot him in the back. Jack then kicks MIB's body off the side of a cliff, killing him. Jack is able to restore the light and pass on the job of protector to Hurley before he dies from injuries suffered in his fight with MIB.
Each of the people in the alternate-L.A. eventually experiences flashbacks which bring back their memories of everything they experienced on the island. It turns out that this is not an alternate reality but rather a type of after-life waiting room. The trials that the Oceanic survivors went through on the island created a strong bond between them and pushed them into becoming better people. Some people died on the island while others left and lived long lives afterward. Because of the bond between them, the Losties' collective consciousness created a place where their souls gathered following their respective deaths. They waited there (and worked out some of their personal issues) until Jack arrived so that they could all move on together.