The sacrifice of a bull and two rams foreshadows the crucifixion, with the bull -- sacrificed for sin -- representing Christ, and the two rams representing the two thieves who were crucified with him. The first ram was slaughtered and completely burnt up, representing the unrepentant thief. He died in his sin and was separated from God eternally. The second ram was still sacrificed, as the second thief still died on his cross, but a portion of the sacrifice, the breast, was given as a wave offering and then served as a feast for the High Priest.
Aaron and his sons were marked with the blood of the sacrifice on the right ear, right thumb, the toe of their right foot symbolizing their role in hearing from God, doing the work of God with their hands, and walking with God.
They were to repeat this process each day, without leaving the tent of meeting, for seven days in order to atone for their OWN sin so that they might then be able to make atonement for the people's sin. This repetition indicates the pervasiveness and recurrent nature of sin. The sacrifice of the bull and rams had to be repeated daily because it was not a permanent atonement.
Finally, Aaron's sons were co-heirs with him of the priesthood. Just as today, believers in Jesus have joined Him in his ministry and partake with Him in both His joy and His suffering (1 Peter 4:13) by following Him. We first follow Him through baptism (Matthew 28:19-20). Then we are clothed with His righteousness (Revelation 7:13-14). We present ourselves a living sacrifice (Romans 12:1-2). The works we do that are temporal will be consumed by fire, but the portion of eternal value will remain (1 Corinthians 3:11-12). And we will feast with the Great High Priest (Revelation 19:9).
In reading Leviticus, it is easy to wonder, "What does this have to do with me today?"