Yoma, Chapter One, Mishnah Eight
This mishnah teaches that on Yom Kippur Temple work which was usually left for the beginning of the day was moved up and done in the night so that the day would be free to do other things.
1) Every day they would remove [the ashes from] the altar at the cocks crow or close to that time, either before or after.
2) But on Yom HaKippurim from midnight, and on the festivals at the [end of the] first watch;
3) And the cocks crow would not arrive before the Temple court was full of Israelites.
Section one: On most days they would remove the old ashes from the altar at the time when the rooster crows, which is at the time when it begins to get light outside, before sunrise. The removal of the ashes is referred to in Leviticus 6:3 and in tractate Tamid, which is in Seder Kodashim (hopefully we will learn this, but not for a few more years). I should note that in the Talmud there is a debate over the meaning of the phrase that I have translated as the cocks crow. Some interpret this to mean an announcement made by a man, who said, Priests get up for your word. In Hebrew the word for cock and the word for man is the same. I will not comment on this.
Section two: However, on Yom Kippur they began to clean out the old ashes at midnight, hours before it got light outside. The Talmud explains that this was because the high priest himself would clean out the ashes and they wanted to give him some time between this work and the rest of the days work. Others explain that they did the cleaning of the ashes early so that they wouldnt have to delay beginning the real work of the day which would come later.
On festivals they cleaned out the ashes even earlier, at the end of the first watch, which means one-third into the night. On festivals there are a lot of sacrifices and therefore there a lot of ashes, so that had to start cleaning out early.
Section three: Finally, on Yom Kippur and on festivals the Temples courtyard would be full of Israelites already by the time the cock crowed, meaning before sunrise. People were so enthusiastic for the days service that they would get there even before the sunrise.