The island was acquired in 1956 by a consortium of American business men and subsequently used as a base for research into eugenics and life extension.
The ultimate aim of this endeavour was to develop technology which could potentially bring about world peace.
The plane crash never really occured and the survivors’ memories are false. The survivors of flight 815, along with the other inhabitants of the island, are the only surviving members of the human race and the so-called ‘monster’ is really a drug-induced hallucination.
The Others are a group of brainwashed cult members.
The ‘incident’ mentioned in the orientation film refers to the accidental release of the genetically modified virus which has caused the mysterious sickness and pressing the hatch button every 108 minutes prevents the outbreak of ‘the sickness’ on the island.
Claire’s father is on the island, working for the Hanso Foundation.
The numbers represent a physical constant which is central to the physics of time travel.