The Day of Atonement, or Yom Kippur, was instituted in Leviticus 16 while the Israelites were wandering in the wilderness. The actions were to be performed by the High Priest. Firstly a young bull and a ram must be sacrificed (Lev. 16:3). Then the High Priest must take two goats and cast lots to determine which would be offered to the Lord and which would be used as a scapegoat. The goat designated for the Lord would then be sacrificed. It was after these actions were performed that the High Priest would then enter the Holy of Holies and burn fragrant incense on the hot coals (Lev. 16:13). It was believed that the smoke that this produced would protect the Priest from death as he was thought to be in the presence of God. The Priest would then take some of the blood from the bull that had been sacrificed earlier and sprinkle it on the Ark of the Covenant and then seven times before the Ark of the Covenant (Lev. 16:14). Indeed, the number seven is considered to hold religious significance due to it symbolising perfection. After these actions had been completed the High Priest would then retreat from the Holy of Holies, without turning his back on the Ark of the Covenant, and complete the ritual in the outer sections of the Temple. The goat chosen to be the scapegoat would be sent into the wilderness after the Priest had laid his hands on its head to symbolise the transference of Israel’s sins (Lev. 16:22).
Although the details recorded in Leviticus were concerned with the ritual which was to be performed in the Tabernacle built in the Wilderness, the festival of Yom Kippur continued to be celebrated during the time when the Jews had their Temple in Jerusalem.
Yom Kippur is still observed today and is considered the most holy day of the year. Despite the Temple being no longer standing, the Jews spend the Day of Atonement, often in their local synagogue, fasting and praying while focusing on the idea of repentance.
Here is a short video which gives a good visual of the actions of the High Priest in the Holy of Holies on the Day of Atonement. We can also see what was said to be contained within the Ark of the Covenant.
Jesus, some Christians may argue, has replaced the Jewish Temple. Indeed, in Matthew 9:13 we are told that Jesus "desires mercy, not sacrifice". Thus, for many, the purpose of the Temple became obsolete after Jesus' death - the ultimate sacrifice. Nonetheless the early Jewish-Christians still respected and visited the Temple. Therefore the Holy of Holies remained a focal point for the early Jesus movement and was significant in New Testament times and in the years until the desturction of the Temple.