From the excellent Compendium of the Catechism of the Catholic Church:
280. In what way is the Eucharist a memorial of the sacrifice of Christ?
The Eucharist is a memorial in the sense that it makes present and actual the sacrifice which Christ offered to the Father on the cross, once and for all on behalf of mankind. The sacrificial character of the Holy Eucharist is manifested in the very words of institution, “This is my Body which is given for you” and “This cup is the New Covenant in my Blood that will be shed for you” (Luke 22:19-20). The sacrifice of the cross and the sacrifice of the Eucharist are one and the same sacrifice. The priest and the victim are the same; only the manner of offering is different: in a bloody manner on the cross, in an unbloody manner in the Eucharist.