Answer: When you realize the size and thickness of the Temple veil, this makes the events occurring at the moment of Jesus’ death on the stake so much more momentous. Matthew 27: 50-51 "And when Jesus had cried out again in a loud voice, he gave up his spirit. At that moment the curtain of the temple was torn in two from top to bottom.”
The veil of the Temple separated the Holy of Holies, wherein dwelt the Ark of the Covenant, the early dwelling place of God’s earthly presence, from the rest of the Temple. Only the High Priest was allowed to enter this area, which he did just once each year, on the Day of Atonement. On that day, the High Priest would make intercession for sin on behalf of the people.
As such, the veil represented the separation between God and man—a separation caused by sin. At Christ’s death, that separation was removed, and mankind could have direct access to God the Father, as symbolized by the tearing of the thick and heavy veil.
Yes, it was Christ’s sacrifice that took away the veil. “But their minds were blinded. For until this day the same veil remains unlifted in the reading of the Old Testament, because the veil is taken away in Christ. But even to this day, when Moses is read, a veil lies on their heart. Nevertheless when one turns to the Lord, the veil is taken away” (2 Corinthians 3:14-16).
Christians today, with the indwelling of the Holy Spirit, have access to God the Father, and are not separated from Him as if by a veil.