The Black Priests are a group of hive-mind telepaths who travel through the multiverse working to make sure incursions between parallel universes are not prevented. Black Swan encountered the Black Priests when she was a little girl, when they attacked the city of her birth during an incursion between her universe and another.
On that very same day, an adult version of the Black Swan and another "Black Swan" traveled to that doomed Earth where they slew two of the Priests in an effort to retrieve an object Black Swan's dead brother had been keeping in his possession before the Priests struck him down.
The Priests, however, followed the two Swans back to the no space from whence they had come and allegedly destroyed the great library in it. Years later, the Black Priests attacked Earth-23099 during an incursion with another universe and came into conflict with that Earth's Illuminati, whom the Priests were able to destroy with ease.
After the fight, the Black Priests learned that they were being watched, and though they never identified who was watching them, the Priests declared that there would be war should anyone, be they Mapmaker, Ivory King or otherwise, attempt to interfere in their schemes. They then destroyed the two Earths without a second thought and left for parts unknown. They were seen again during two different Incursions that the Black Panther of Earth-616 had been monitoring via The Bridge.