The Mass is the manifestation of the Great Love of God for mankind. He first sent his Son into the world to die for our sins and He now makes it possible for his adopted children to offer Christ, his only Son, as the acceptable sacrifice throughout the ages for the salvation of mankind.
The Sacrifice of Christ on the Cross and that of the Eucharist are one and the same sacrifice but now this sacrifice is offered in an unbloody manner. Christ becomes truly present in his humanity and divinity, when the priest says the above words.
The sacrifice of Christ is directed to intimate union of the faithful with Christ in Holy Communion.
The final purpose of Christ's Sacrifice is to give honor and glory to the Father as expressed by the priest in the doxology:
Through Him, with Him, in Him,
in the unity of the Holy Spirit,
all Glory and Honor are yours,
almighty Father, forever and ever. Amen.