The Old Testament sacrificial system points forwards to Jesus Christ
The Law that God gave to the Israelites through Moses included a list of things they were to do and not to do - for example, the Ten Commandments.. There was also a complicated code of sacrifices that they had to make when they broke the Law. These sacrifices were a way of dealing with their guilt. Many of the sacrifices involved the death of an animal - a sheep or a cow, for example. The animal had to be killed in a defined way, and the body often had to be burned on an altar. This system of animal sacrifices points to the need for a death to take away sin and guilt.
However, the sacrifices in the Old Testament could never completely meet this need. Rather, they point forward to the one perfect sacrifice of Jesus.The New Testament picks up this theme. For example, the New Testament specifically picks up the Passover lamb as a picture of the sacrificial death of Jesus for the sins of his people - see 1 Corinthians chapter 5 verse 7.
This is what the New Testament writer of 'Hebrews' says about Christ and the Old Testament sacrifices:
So for the writers of the New Testament, the central reality is Jesus's sacrifice of himself on the cross to deal with the sin and guilt of his people. The Old Testament sacrifices were models or illustrations that pointed forwards to this reality, but they could not themselves deal with guilt and sin. Next.
For more about how the whole Bible points to Jesus - Old Testament as well as New Testament - read Vaughan Roberts' excellent 'God's Big Picture: tracing the story-line of the Bible', or Graeme Goldsworthy's 'According to Plan: the unfolding revelation of God in the Bible', or Alec Motyer's 'Look to the Rock: An Old Testament Background to our understanding of Christ.'