Quarantine is the process of isolating people or objects that might be carrying contaminants such as diseases, chemicals or radioactivity. It is also the name given to the time period in such isolation while tests are conducted to find out if such contamination exists.
The word "QUARANTINE" was first seen stenciled on the hatch door to the Swan station. It was later also seen stenciled on the Arrow station entrance, but notably not on any of the other DHARMA stations seen.
The survivors of Flight 815 linked the word with the Sickness described by Danielle Rousseau. When Aaron fell sick in "Maternity Leave", Kate stated: "Claire thinks he's sick, as in 'quarantine' sick".
In "Live Together, Die Alone, Part 2", Kelvin wore a biohazard suit, and told Desmond he had to wear it outside the station to avoid becoming sick. He asked Desmond "You want to go out there with the quarantine and the Hostiles?" Desmond later learned that this was, at least in part, a ploy by Kelvin.
There is a possibility the quarantine warning may be related to the vaccine or the toxic gas released at the time of the Purge. ("The Man Behind the Curtain") ("The Constant") According to the Lost Encyclopedia, Radzinsky quarantined himself inside the Swan, fearing that the toxins used in the Purge would harm him. It was during this time that he decided to draw the blast door map.
It is also possible that the quarantine for the Swan site could be related to leakage of electromagnetic energy outside.
In a flat in St. Germain de Pres, France, Rachel Blake found a folder left for her by Darla Taft. Inside, amongst other items, she found schematics for a hospital ship, named the Helgus Antonius. She worryingly noted that the wards on the ships were marked "quarantined".
The official Lost jigsaw puzzles contained a book code cipher on the back of one puzzle. After translating it using The Turn of the Screw, one message, written by Kelvin or Radzinsky, is "QUARANTINE IS A HOAX".