The Apocralypse is the end of the world, so named because it is an apocryphal apocalypse, nobody is sure when it will happen, how it will happen, and whether it will happen in the here-and-now sense. The Tea-Time of the Gods, when the Ice Giants will march against them for the last time, probably without even giving them the lawnmower back first. The End of the Disc, when the Four Horsemen (DEATH, WAR, FAMINE and PESTILENCE) will ride forth. In the older Books of Omnianism, there is also an Angel clothèd all in white with an iron book who presides over the event, and such an angel has come into existence, and has been waiting for this event for centuries. However, by the time the event occurred, he was dismissed as an allegory for something that had already happened. This knowledge had no discernible effect.
The Apocralypse has almost-happened in The Light Fantastic, Sourcery (thanks in no small part to Rincewind) and Thief of Time. Almost. Somehow the events turned around. In Thief of Time, Kaos, the Fifth Horseman also rode, though the Ice Giants went unmentioned.
The Roundworld reference, of course is to the The Apocalypse (no 'r'!), the force of man's destruction described in the Christian Bible in chapter six of the Book of Revelation, the Original Greek Αποκαλυψις Ιωαννου (Apokalupsis Iōannou), "Revelation Of John". The four horsemen in this account are traditionally named after the powers they represent: War, Famine, Conquest, and Death. However, this is slightly at odds with the conventional interpretation of the Bible, which actually only directly names the fourth: "Death".