The 'Purification' Ceremony is a ritual performed by Horde Prime when he wished to 'recondition' members of his Clone Army if one were to show a 'flaw' (e.g., any form of personal identification, such as a name).
Details regarding this event are obscure, as it has only been confirmed to have been conducted on two individuals, Hordak and Catra, and of these two, only Hordak was seen being taken through the ceremony. What is known is that it appears that the victim must be submerged in a green, phosphorescent liquid, which goes on to emit an immense electrical surge through it, sending energy coursing through the unfortunate soul's body as the liquid around it glows, finally ending in the victim being connected to the hive mind (assuming they have been already chipped). This, however, is not the only way to place a victim under Prime's control via a Horde Chip, as made clear by Scorpia, Mermista and so many others chipping during the invasion.
Though unconfirmed, the 'Purification' Ceremony might be a ritual reserved for 'purifying' clones and those who have gained Prime's personal enmity, but he wishes to keep for one reason or another (Prime openly admits that, prior to her desertion, his hopes for Catra had been high).
