The Sanctuary that Moses built was the Sanctuary of the "Old Covenant" (see Hebrews 9:1-14). The true Sanctuary in heaven, of which Paul speaks of in Hebrews 8:1, 2, is the Sanctuary of the "New Covenant".
All the animal sacrifices during the Old Covenant Sacrificial System represented the True Sacrifice, Jesus. The Old Covenant used figures to portray what the New Covenant would do because of the blood of Jesus, the Real Sacrifice. His blood, alone atones for our sins, it was never the blood of an animal but the blood of Jesus that takes away our sins.
Another way of saying this is that in the Sacrificial Services of the Old Covenant, an innocent animal representing Jesus, took the place of the sinner and died. In the Sacrificial Service of the New Covenant, our innocent God, Jesus, took our place and died as a sinner so that we may live without sin.
For further study, read:
The Law and the Covenants
What is the Sanctuary?
In the Holy of Holies