The Incident, first mentioned by "Dr. Marvin Candle" in the Swan Orientation film ("Orientation"), was an electromagnetic anomaly that caused a catastrophic event at The Swan construction site. The Incident occurred on the fourth day following the Oceanic Six's return to the Island in July of 1977, when a drilling accident at the site of the Swan station unleashed a pocket of electromagnetic energy. While the Swan Station was originally being built to harness this energy, the DHARMA Initiative was forced to construct The Swan to contain the energy with large amounts of concrete, using the protocol to regulate the anomaly.
However, doubt has been cast on an electromagnetic anomaly being the cause of The Incident. It was briefly suggested by Miles that the survivors' plan to detonate the core of a hydrogen bomb (itself a fission bomb) at The Swan construction site might actually be the cause of The Incident, not the anomaly. Daniel Faraday suggested that detonating a nuclear device might prevent the electromagnetic anomaly, beginning a chain of events which ultimately results in Oceanic Flight 815 not crashing on The Island. His theory contradicted his earlier theory that events of the past cannot be altered. Currently, the predictions of Miles and Faraday each appear to be correct in different realities.
Main Article: The Incident, Parts 1 & 2
Due to his discovery in Ann Arbor of a photo of the new recruits in 1977 including Jack, Kate, and Hurley, Daniel Faraday returned to the Island, and warned the survivors of a catastrophic event he believed was imminent. He convinced Pierre Chang that he was from the future and had knowledge of the accident, and he revealed to Jack that he believed it could be avoided by detonating a bomb, taken from Jughead's core, at the Swan construction site.
Upon his arrival at the Swan construction site on the fourth day after the survivors arrived in 1977, Chang tried to convince Radzinsky that drilling into the pocket of energy could unleash a catastrophic anomaly, but Radzinsky refused to cooperate. A violent struggle erupted, but Jack, Miles, Juliet, Sawyer and Kate gained the upper hand over Radzinsky's team, allowing Jack to drop the the plutonium core taken from Jughead into the drilling pit at the same time the construction team's drill hit the energy source. Although it did not detonate immediately, Juliet, injured by a fall into the pit, was able to strike the bomb several times with a rock. An immediate white flash of light followed the 8th hit, apparently detonating the bomb and creating two separate realities. ("LA X, Parts 1 & 2")
During the Swan Orientation Film, Dr. Marvin Candle mentioned that there was "an incident" which resulted in the creation of a protocol that required a code to be entered every 108 minutes. The incident involved a leak in the containment associated with an electromagnetic anomaly. The leak caused an unspecified charge to build up within the anomaly. As the charge built up, the magnetic field associated with the anomaly grew. After 108 minutes, the magnetic field was large enough to damage the Swan station. ("What Kate Did")
Dr. Marvin Candle issued a strict warning not to use the computer for communication with the outside world. He went on to say that failure to comply would compromise the integrity of the project and could result in another incident. Candle also seemed to indicate that the incident occurred shortly after the Swan station began operations. ("What Kate Did")
Daniel Faraday explained that during construction of the Swan, the workers drilled into the magnetic force, causing a catastrophic discharge that required the protocol to be enacted. The protocol was created so that the magnetic anomaly could be discharged every 108 minutes, thus preventing an electromagnetic catastrophe. Failure to comply with this protocol leads to a system failure. There is a failsafe mechanism in place below the floor of the computer room that will destroy the Swan and permanently and safely seal the electromagnetic anomaly. ("Live Together, Die Alone")
It is worth noting that apparently counter to what Pierre Chang alluded to (that the station was "originally" a laboratory used for research), the Swan's protocol was established during the construction of the Swan itself due to the workers drilling into the magnetic energy field. This would seem to suggest that there wasn't even a brief period of time that the Swan was used for its original research purpose. However, it's not clear yet whether or not this is the same mysterious Incident that Chang spoke of.
The blast door map contains the following references to incident(s):
A commonly accepted theory is that "MDG" stands for the DeGroots, which leads to speculation that the DeGroots split from Alvar Hanso or that both came into conflict together with an unmentioned third entity. However, it is unclear what the "M" before "DG" would stand for since the DeGroot's names are Gerald and Karen. Another likely suspect is that the "M" stands for "Mittlewerk".
MDG may refer to "magnetic DeGaussing."
In the videogame Lost: Via Domus, Elliott Maslow discovered "The Incident Room" on the other side of the concrete wall. The Incident Room was accessed by a tunnel and a large locked door near the exterior of the Swan.
The room contained a large reactor amongst a room full of severely damaged equipment. The reactor was tilted to one side, and discharged electricity and a fluid that looks like water. The reactor had the appearance of two large electromagnetic coils suspended over an excavation into the Island. Unlike the Swan, the Incident Room's machinery was in a state of disrepair, possibly due to the Incident. The Incident Room also had its own computer, much like the Swan's.