Yoma, Chapter 1, Mishnah 8. In the previous mishnah we learned that they would keep the Kohen Gadol awake until the time arrived for slaughtering the daily tamid offering. However, the first act performed in the Beis HaMikdash, even before the slaughtering of the tamid, was terumas hadeshen - the removal of the ashes from the altar, which is a mitzvah from the Torah. Our mishnah opens the discussion of terumas hadeshen and its proper time.
The time of terumas hadeshen on an ordinary day:
"Bechol yom tormin es hamizbe'ach bikri'as hagever, o samuch lo, bein lefanav bein le'acharav" - every day they would remove the ashes from the altar at the time of kri'as hagever, or close to it: slightly before it or slightly after it.
What is "kri'as hagever"? Two explanations are given:
The crowing of the rooster.
The announcement of the kohen, who would announce the time at which the kohanim were to begin their service.
The change of time on Yom Kippur and on the festivals:
"V'yom haKippurim mechatzos" - on Yom Kippur they moved terumas hadeshen up to midnight. The reason: a great many services rested upon the Kohen Gadol, and out of concern for his weakness - that he would find it difficult to perform everything required of him - they sought to get as much as possible out of the way as early as possible.
"U'varegalim me'ashmurah harishonah" - on the three festivals, Pesach, Shavuos and Sukkos, they would do this even from the first watch, that is, after a third of the night had passed. The reason: apparently terumas hadeshen also included gathering all the ashes that had accumulated from the offerings, in addition to the mitzvah of terumas hadeshen itself. On the festivals a very large number of offerings were brought during the day, and the activity lasted longer, and therefore they moved the time up even further.
"V'lo haysah kri'as hagever maga'as ad shehaysah ha'azarah me'le'ah miYisrael":
By the time kri'as hagever arrived - whether that means the crowing of the rooster or the announcement of the kohen, at daybreak - the Courtyard was already full of Jews who had come ready to bring their offerings. This is so if we explain that this statement refers to a festival. Others explain that this last statement refers to Yom Kippur, when people came to watch the service of the Kohen Gadol.
In summary: in this mishnah we learned the times of terumas hadeshen - the first act in the Beis HaMikdash, preceding the slaughtering of the tamid: every day at kri'as hagever or close to it, on Yom Kippur from midnight because of the great amount of service required of the Kohen Gadol and the concern for his weakness, and on the festivals from the first watch because of the great number of offerings. We also learned the two explanations of "kri'as hagever", and the testimony of the mishnah that already before this time the Courtyard was full of Jews.