At the Last Supper, when Christ offered bread and wine, He intended to leave His Church a memorial of His sacrifice on the Cross. Through this memorial, His sacrifice would not only be represented but also its saving power would be communicated to His disciples for all time.
The sacrifice of the Eucharist is a memorial of the sacrifice on the Cross, but not merely in the sense of recalling a past event. Instead, it actually makes the sacrifice present, as Christ Himself is truly present under the outward signs of bread and wine, continually offering Himself in sacrifice to the Father.
The sacrifice of the Eucharist is therefore one and the same as the sacrifice of the Cross:
However, in the Eucharist, Christ now offers Himself through the ministry of His Church and under the outward signs of bread and wine.