The Ceremony is a ritual that is performed at the academy by The Faculty and special students. Very little has been revealed, other than the involvement of brown robes, a sacrifice, and an altar. The first confirmed instance of "The Ceremony" is seen after Woodrun after The Truants shunted all the students into the future.
Jun Fukayama, in his guise as Hisao, wanted to perform the Ceremony to set everything right. Howard, a fellow student, had misgivings about performing the ritual without having a teacher present. Jun retorted that they were taught the way for a reason, and this was their chance to prove themselves worthy. In this instance, the sacrifice is to be a ram, the school mascot.
When Ike and Hunter sneaked out of their room during their first night at the Academy, they interrupted a similar ritual involving Reginald Gribbs and other students clad in brown robes that appears to be timed to coincide with the Glories' arrival. However, this has been strongly implied to not be the same ritual as "the Ceremony".
Jun says that the ceremony only requires two people and a sacrifice.
Part of the ceremony is heard:
"Accept this sacrifice--Hear your follower's cries--Set right what has been made wrong--And lead us--"
The ritual is similar to the biblical account of Abraham who was instructed by God, as a test of faith, to sacrifice his only son, Isaac on an altar. Abraham obeyed, and was about to kill Isaac when an angel interrupted him at the last minute. Abraham freed Isaac, and proceeded to sacrifice a ram which was caught in a bush instead.