The Cleansing is an event that marks the end of one iteration of The Cycle and occurs when a Beacon is lit without a Numinos at its core. It's characterized by the sudden disappearance of all conscious living beings of a civilization, who are amalgamated into a new High One.
The Cleansing occurs when a Beacon is lit without a Numinos, and hiding this information is vital for the High One's plans. The High Ones make the Emissaries believe that the activation of a bare beacon will simply cause an explosion, and leads the one known as "Emperor" to do so after missing their chance of getting a Numinos, for fear of failure. In fact, it is the very triggering of the cleansing that leads to its execution by the ones trying to stop it, a form of Self-Fulfilling Prophecy.
When the Beacon is lit without a Numinos, all the energy stored in the Black Stones is scattered about, creating a flash of light at the center of the Beacon's core that then starts to envelop the sky. In mere hours that light has enveloped the whole world. Any conscious living creature within reach of this light has their consciousness slowly removed from their body, and at the end of the process only a grey carcass is left behind, as seen in the very first vision of The Prophet. The Emissaries are also affected by the light, but its effect is slower on them. This is one of the factors that allowed The Prophet to destroy the beacon before the Cleansing was complete.
All the devoured consciousnesses are then conjoined to make a new High One, and for that reason it is said that the High Ones are made of "pure memories" or, sometimes, of "pure death".
There are two main ways to prevent the Cleansing.
The first one is to simply forfeit one's living body and transfer into a mechanical one, a process known as Apotheosis. Since the cleansing only affects living beings, transferring one's consciousness to a mechanical being "tricks" the light into letting one live. This is the same principle behind the slowing down of the effect on Emissaries, since they are technically not alive, but still have an organic body, and therefore still suffer the effect eventually.
The second one is still unknown, but can be used to shield entire cities from the event. This method was devised by the Starlings, who lived on a city in the skies documenting all the cleansings.