The day of atonement (or “day of coverings”) involved a re-investiture of the priest. At the beginning of the rite, he removed his garments of glory (Leviticus 16:3) and at the end of the day he put them back on (16:23-24). Before the rites, he bathed his body (16:4) and again after the rite (16:24), a double baptism that recalled his baptism at his ordination (Exodus 29:4; Leviticus 8:6). (There is a dramatization of this aspect of Yom Kippur in Zechariah 3.)
The day of atonement was also a re-boot for the sanctuary. That is evident in the fact that the rites of Yom Kippur removed the sins and uncleanness of the people of Israel (Leviticus 16:21) and purified the inner sanctuary. No other rites of cleansing penetrated so far into Yahweh’s presence.
It’s also evident in the fact that Aaron worked alone in the sanctuary, surrounded by incense smoke, throughout the day: “When he goes in to make atonement in the holy place, no one shall be in the tent of meeting until he comes out” (16:17). When the tabernacle was first consecrated, the glory-cloud of Yahweh descended on the tabernacle and filled it so that no one could enter (Exodus 40:34-38) and the same happened at the dedication of the temple (1 Kings 8:10-11). Yom Kippur was not exactly the same, because one man was allowed into the temple. Still, the allusion to the sanctuary dedication is there, and indicates that the temple system was restarted each year, along with the priesthood.
If Jesus’ death and resurrection is the final day of atonement, this is what it a achieves: A final renewal of priesthood and temple.