In the Old Testament each year a spotless lamb was sacrificed to purify the people. The sins of the people were washed clean by the sacrifice of blood.
This lamb is a visual representation of the Messiah Jesus who was to come. It is no surprise then John the Baptist a messenger appointed by God to pave the way for the Messiah exclaimed:
"Look the Lamb of God who comes to take away the sins of the world."
You see Jesus is the fulfillment of the old covenant. Many people see Jesus as issuing a new covenant and it is partly right but his new covenant is more a permanent fulfillment of the old.
Since he has fulfilled the covenant perfectly much of the old covenant is modified and looks very different. But really the covenant is more of a continuity than a separation.
It is simply that Jesus fulfilled everything once and for all so a large number of repetitive elements are ended. The discontinuity is because of the efficacy of the sacrifice making parts of the old covenant obsolete.
The continuity is far greater than most people see. At first the discontinuity seems greater but as you look you can see the continuity far out ways the discontinuity and the discontinuity is based on the efficacy of Jesus' work.