The sacrifice of Yom Kippur is separate and distinct from all the other sacrifices offered during the year. While the others reconciled the sinner on a day to day basis with God, Yom Kippur is the day that God would forgive all the sins of all the people in every generation – in essence this was their salvation sacrifice.

Yom Kippur is the only time that the High Priest would enter into the presence of God in the Holy of Holies, doing this four times in all that day. He would remove four of his eight garments – all those with gold – He would change his clothes five times, dipping himself in a Mikveh each time.Special offerings were made in addition to the regular ones:
An offering for all the people paid for with public funds (Korban Mussaf) The High Priest’s personal sacrifice paid for with his own money

The two goats – one sacrificed to Hashem and the other sent to Alazel after all the sins of the people were “placed” upon it The High priest would turn to the curtain separating the Holy Place from the Holy of Holies, and sprinkled the blood of the bull sacrifice one time upward, then seven times downward. He would repeat this process with the blood of the goat sacrifice one time upward, then seven times downward.He then entered the Holy of Holies, took blood from the bull and the goat and put some on the four corners of the threshing floor. He also sprinkled this on the altar, repeating the process of sprinkling once upwards, then seven times downward.

The miracles/signs that took place, showing God’s approval and forgiveness:

Drawing of lots always produced “LaHashem” in the right hand
The red ribbon tied to the scapegoat always turned white
The Center light of the Menora always burned until morning
Fire on the copper altar never went out even when it wasn’t properly stoked
Priests felt full even after eating only a small part of the offerings
The smoke of the incense offering would fill the Holy of Holies

The Talmud however, records that many of these miracles ceased to occur about 40 years before the destruction of the second Temple, and never returned. This of course coincides with the time of the death of Yeshua:

Yoma 39b – During the last forty years before the destruction of the Temple the lot [‘For] did not come up in the right hand; nor did the crimson-coloured strap become white; nor did the westernmost light shine; and the doors of the Hekal would open by themselves, until R. Johanan b. Zakkai rebuked them, saying: Hekal, Hekal, why wilt thou be the alarmer thyself? I know about thee that thou wilt be destroyed, for Zechariah ben Ido has already prophesied concerning thee: Open thy doors, O Lebanon, that the fire may devour thy cedars.