This demon, Lilith, is trying to break the 66 seals to free Lucifer from Hell. Lucifer... will bring the Apocalypse. So... smoke 'em if you got 'em.
In Supernatural, the Apocalypse is a series of disastrous events leading up to and including the end of the world.
Soon after Dean's resurrection, hunters are attacked by the ghosts of people they could not save. Bobby's research uncovers an obscure translation of the Book of Revelation that lists the ghosts, or the Witnesses, as a sign of the upcoming Apocalypse. Castiel confirms that demons, under Lilith, are attempting to break the 66 Seals and free Lucifer from his prison.
The Winchesters, Bobby, and angels fight to stop other seals from breaking, but they steadily lose ground. There are over 600 seals, however, only 66 need to be broken. They discover that the first seal was broken by Dean in Hell, when he became a torturer. Sam feels compelled to kill Lilith, who he has been told is the only being that can break the final seal, while angels tell Dean that it is he who must prevent the Apocalypse.
In fact, the higher ranking angels including Michael, Raphael and Zachariah want the Apocalypse, and hold Dean in the Green Room while Sam seeks out Lilith with Ruby. Castiel frees Dean and sends him after Sam, but Sam kills Lilith, whose death is actually the final seal. Lucifer's cage opens, and the Apocalypse begins.
Immediately, Sam and Dean hear of earthquakes and disease spreading. Zachariah confronts the brothers, and reveals that the real carnage will not start until Lucifer enters his preordained vessel.
Zachariah: Lucifer is powerful in ways that defy description. We need to strike now, hard and fast—before he finds his vessel.
Sam: His vessel? Lucifer needs a meat suit?
Zachariah: He is an angel. Them's the rules. And when he touches down, we're talking Four Horsemen, red oceans, fiery skies—
Zachariah also reveals that Dean alone cannot possibly kill Lucifer, but he tells Dean that he is Michael's vessel, and once occupied, he can defeat Lucifer. Once Lucifer is defeated by Michael believes the world will end allowing him to create paradise. Sam learns later, from the Devil himself, that he is Lucifer's true vessel. Neither brother is willing to consent to serve as a vessel, postponing the final battle. Michael remains disembodied, but Lucifer finds a temporary vessel in Nick.
Demons fall in line behind Lucifer, and his plans proceed. He intends to destroy humanity, and essential to his goals are the Four Horsemen of the Apocalypse. War is the first encountered by Sam and Dean. He causes an entire town to believe there are demons among them when there are none. Famine, a weakened but still intimidating figure, is cared for by demons at Lucifer's direction. Pestilence, again assisted by demons, devises a scheme to spread the Croatoan virus as fast as possible. Death is imprisoned when the Apocalypse begins, and Lucifer soon finds a way to set him free and force his obedience. With Death under his control, Lucifer orders still greater disruption. The Whore of Babylon also serves as an instrument of destruction and misinformation. Jesse Turner, the Antichrist, was supposed to play an important role during the destruction of Earth, but he decided to turn away from Lucifer's plans.
Sam and Dean follow omens, from forest fires to biblical storms to the dead rising, and combat what they find. Other hunters are hostile toward them because it is rumored that they are directly responsible for starting the Apocalypse. They are constantly assaulted by both angels and demons who want to force them to serve as vessels so that the final battle between Michael and Lucifer may take place; all parties involved claiming that it is their destiny. They try and fail to kill Lucifer, losing Ellen and Jo in the process. Dean, slowly worn down by the ominous warnings of others and afraid that Sam will give in, and that Lucifer will win, decides to say yes to Michael, but the efforts of Sam, Bobby, and Castiel keep him away from the archangel until he decides to keep fighting. Michael then takes Adam, Sam and Dean's half-brother, as his host.
When they learn from Gabriel that Lucifer can be re-imprisoned using the rings of the Four Horsemen, Sam, Dean, and their allies do whatever is necessary to acquire the rings. Sam comes up with a plan to say yes to Lucifer, so that the archangel will enter him and he can throw himself into the pit. Team Free Will is reluctant to agree, but does so. Sam takes Lucifer in, but cannot control him. They go to the confrontation with Michael. Dean interrupts, and manages to reach Sam, who opens the portal and tips himself, Lucifer, Adam, and Michael, over the edge. The Apocalypse is stopped.
Following soon after the events of 5.22 Swan Song, a civil war breaks out in Heaven. Raphael, the leader of the traditionalists, intends to free Michael and Lucifer so that the Apocalypse will restart and the predestined end of the world can still be reached. Castiel opposes him, and is the victor.
The term "apocalypse" is Greek in origin, and means "revelation"; the Book of Revelation is the last in the New Testament. It is a vision of the end times that relates specific milestones that correspond to the opening of seals in the book of judgment. The first four seals release the Four Horsemen of the Apocalypse. The fifth concerns martyrs, and after the opening of the sixth seal, disasters begin. When the seventh seal is opened, lightning, earthquakes, hail and fire, the burning of trees, mass extinction, poisoned waters, and monsters plague the earth. The Whore of Babylon appears in verse 17:5, and the imprisonment and escape of Lucifer are in chapter 20.
A discussion of the end of days or Judgment Day appears in Judaism, Christianity, and Islam, though interpretations and signs vary.