The End of Days (also known as the End of the World, Armageddon, the Apocalypse) is a concept within DEXTER. The End of Days is a religious concept mentioned heavily within the Book of Revelation as the end of an old world while bringing birth to the New World. In simple terms, everyone will die and the world as it is known will utterly change. Specifically, in Season Six, the End of Days has become a common theme as Travis Marshall seeks to bring about the tribulation, by enacting Tableaus deciphered from notes taken on the Book of Revelation.
Travis seeks to bring this Armageddon by creating seven sacrifices that should trigger the End. If he is successful, then the world will go through a drastic change. However, this outcome is unlikely from a scientific point of view. Regardless, the actions of Travis and "Professor Gellar" have created a legion of followers whom believe that the End is coming. Fear and paranoia are rampant in Miami though it is unknown how the rest of the world is viewing the Doomsday Tableaus.
According to the Book of Revelation, on the 1260th day following the appearance of the Two Witnesses, the End will be triggered. However, also according to the book, "the Beast" is said to overcome and kill the Witnesses before they will be resurrected by God.
The actual date (in the DEXTER storyline) is Monday November 28th, 2011 when the solar eclipse was meant to happen. Travis attempts to complete the prophecy by slaughtering the Lamb, which turns out to be Harrison Morgan the son of Dexter Morgan. Dexter arrives in time to save Harrison's life, leaving Travis with a short time frame to first kill "The Beast" and then slaughter the lamb. Of course, Dexter is able to overcome Travis at this point and the eclipse occurs, then ends shortly thereafter.
In conclusion, Travis was unsuccessful in bringing about the true End of Days but the Beast does succeed in "slaying the Witness" when Travis's life is taken by Dexter's blade. Regardless, the events continue as a developing story and lead into Season Seven.