The Swan

Lostoctagon2hr — Octagon logo found inside the station

The Swan is one of the stations built by the DHARMA Initiative on the island. Earlier in the series, it is only referred to as "The Hatch".

Facts

The Orientation Film in Orientation reveals the identification of facility is "Station 3".
The initial food rations are enough for one man for three months.
Has water piping and plumbing systems
A section has been sealed off with concrete that is several feet thick (possibly after the incident mentioned in the Orientation Film). The magnetic source behind the concrete is strong enough to attract the key around Jack's neck.
The surface-level exit of the hatch has The Numbers engraved into it. The inside of the hatch (not visible from the outside) has "QUARANTINE" spray-painted on it.
Contains items which appear to originate in the 1970s, such as a lava lamp, LP records, a geodesic dome and monochrome computers.
Some modern items can also be found in the bunker, such as a late-model washer and dryer set (Whirlpool Duet).
Desmond claims he was brought to The Hatch by Kelvin, and had been living there for some time when the plane crashed.
Contains an elaborate security system that makes use of mirrors to see around corners.
Contains an armoury that holds an arsenal of pistols, rifles, and other weapons. The combination known only by Jack and Locke. Sawyer later conned Locke into removing the weapons.
Contains blast doors which retract into the ceiling. These doors appear to be able to isolate the dome from the living quarters. The doors descend after the speaker system counted down in Lockdown. A hidden map can be seen by black light on one of the doors.
There is a mural inside featuring abstract figures and incorporating the number 108.
The Dharma Ranch Dressing Hurley stashed is labeled good for seven years (after opening) at room temperature.
In all of the food and the antiseptic liquid from Swan, the following code is seen: DI 9FFTR731.
There is a fan-made map of this Station.

About the name

"The Swan" is the name of an Elizabethan theatre in London (used by Shakespeare).
SWAN Instruments are instruments that can be used to measure electromagnetic fields [1]. According to the Orientation Film, The Swan was used for projects involving electromagnetism.
The constellation of Cygnus is also known as "The Swan". There is an asterism) called "The Arrow". Mythology states that Hercules is firing the arrow at either Cygnus or Agilla, "The Eagle". A companion constellation to Cygnus is Lyra, "The Lyre", which is the harp that Orpheus uses to con his way into Hades, according to legend, but was previously known as "The Vulture", according to Ptolemy.
Possibly named after Sir Joseph Wilson Swan an English physicist and chemist.
HMS Swan was an Australian Navy ship launched in May 1935, subsequently decommissioned and sold for scrap to Hurley and Dewhurst of Sydney.
HMS Swan (DE-50) is now a dive wreck and artifical reef 1.3 nautical miles off Point Picquet, Western Australia.
The Swan is a short musical composition for cello and piano from Carmille Saint Saens' "Carnival of the Animals".
The Sanskrit word for swan is hamsa or hansa, which sounds similar to Hanso

Cultural references

Swans are revered in many religions and cultures, especially Hinduism. The Sanskrit word for swan is hamsa or hansa, and a swan is the vehicle of many deities (such as the goddess Saraswati). Swans are mentioned several times in the Vedic literature, and some swans have also been said to have the knowledge of the Supreme Being Brahman. They are said to reside in the summers in the Manasarovar Lake and migrate to Indian lakes for the winter, eat pearls, and separate milk from water in a mixture of both. Hindu iconography typically shows the Mute Swan. It is wrongly supposed by many historians that the word hamsa only means a goose, since today swans are no longer found in India, not even in most zoos. However, ornithological checklists like this clearly classify several species of swans as vagrant birds in India.

Pandora's Box

Hurley asks Locke what he thinks is in the hatch. Locke responds, "Hope."

When Hurley tells Leonard that he used "the numbers" to win the lottery, Leonard says, "You've opened the box."

(from Wikipedia) Epimetheus told Pandora never to open the box she had received from Zeus. However, one day, Pandora's curiosity got the better of her and she opened it, releasing all the misfortunes of mankind (plagues, sorrow, poverty, crime, etc.). Once opened, she shut it in time to keep one thing in the box: Hope. The world remained extremely bleak for an unspecified interval, until Pandora "chanced" to revisit the box, at which point Hope fluttered out.
With this in mind, perhaps the "chance" that the crew needs to take is to let the numbers count down in order to release this hope. This theory was derived from the possible meanings of the Hieroglyphics that were briefly shown. One of the possible meanings is "depart" or "proceed" depending on the final symbols. (However for this meaning to be possible, the last counter symbol would have to be different from the one that was locked in). See Alternative_Translations

Theories

Thehatchoutside — The hatch was the big mystery in the first season

The station could have been named The Swan because of its shape (large underground bunker with a long tunnel to the surface on one end). It could also have other meanings that are not fully understood yet.
The station may be a very complex version of a Skinner Box
The mural is painted in the same style as Thomas' artwork
There is a red lava lamp in the Swan similar (if not identical) to the one in Thomas' apartment... but how could he have been in the Swan if we last see him only a couple of months before the crash?
Are the data tape machines fake? To have reel-to-reel data recorders that close to such a powerful source of magnetism is risky if the data is needed.
The supply deliveries could explain the modern items
See "Stations" for more theories on all the stations
The source of magnetism is a bigger monster.
Could also refer to Ingo Swann, an artist who helped develop the procedure of remote viewing at the Stanford Research Institute, and has become well known as a remote viewer himself. Swann is commonly accredited with proposing the idea of Coordinate Remote Viewing, a process in which viewers would view a location given nothing but its geographical coordinates, which was developed and tested by Hal Puthoff and Russell Targ with CIA funding.
Could have a nuclear reactor behind the concrete to power the island. The computer could be for operating it. The Station 3 Protocol could be for controlling it (inserting the control rods to prevent meltdown) Most of the Station 3 inhabitants would not be nuclear-operators, so they had to make it foolproof. Possibly the numbers can be skipped once or twice without dire effects. The Incident could be a nuclear accident that rendered part of the island contaminated by radiation and be responsible for The Sickness. The Lockdown Incident might be part of the refueling procedure. The Orientation Film might be deliberately vague about all this because most inhabitants would likely be uncomfortable living next to a reactor, and also communication with the outside world might lead to unwanted attention from the likes of the UN Security Council among others. Also the CR 4-81516-23 42 vaccine might be Potassium Iodine, which can help protect against radiation. To be effective, Potassium Iodine must be administered every 24 hours, unlike normal vaccines. Taking shots of CR 4-81516-23 42 seemed to be part of Desmond's daily routine.
On the Blast Door map, all of the hatches seemed to have passages that would have connected to the question mark station in the middle of the map. However, they all were crossed out about halfway. However, the passage seems to continue exclusively in the Swan, after the X the corridor continues, but the walls are only represented by dotted lines, until it comes to a smaller question mark. Therefore the Swan may be the only hatch that connects to the central question mark. This corridor may be blocked by the wall that Jack's key was magnetically attracted to.