The highlight of the the Yom Kippur Temple service is the entry of the Kohel Gadol into the innermost chamber of the Temple, first to create a cloud of incense (symbolically causing God's presence to appear), and then to sprinkle the blood of the bull and goat sin-offerings (as with every sin-offering, sprinkling blood is what causes or symbolizes the atonement; the unique part of the Yom Kippur sprinkling is its location). Through the sprinkling, atonement is achieved for the Kohen Gadol himself (through the bull, which belongs to him), and for the Jewish people (through the goat, which is taken on behalf of the entire people).
It is interesting that exactly one action is performed to the bull, and one to the goat, before their slaughter and blood-sprinkling. Regarding the bull, the Kohen Gadol must confess his sins. Regarding the goat, there is no confession. The only action performed is the drawing of lots, which distinguishes the goat which will be offered as a sacrifice from the goat which will be sent to the desert.
The sin-offerings of the Kohen Gadol and the people represent the different methods by which individuals and the Jewish people achieve atonement. The Kohen Gadol, like every individual, must confess his sins and repent in order for his sins to be atoned. But for the Jewish people as a whole, this is not necessary. The goat becomes a valid sin-offering simply by the fact that the lots chose it over the other goat. And our collective atonement is achieved simply by the fact that God has chosen the Jewish people.
Of course, the Temple service achieves atonement - "kapparah", as is mentioned repeatedly. This consists of God's renouncement of the right to punish us. But there is another purpose to Yom Kippur: "taharah", moral purification. Kapparah is repeatedly mentioned throughout the description of the Temple service. Taharah is mentioned mainly at the end of the chapter, in conjunction with the command to "afflict your soul" on Yom Kippur. The Temple service spares us from punishment, but only through soul-searching and repentance can we become better people.