The Catechism of the Catholic Church notes:
1362 The Eucharist is the memorial of Christ's Passover, the making present and the sacramental offering of his unique sacrifice, in the liturgy of the Church which is his Body. In all the Eucharistic Prayers we find after the words of institution a prayer called the anamnesis or memorial.Anamnesis refers to a specific part of the Mass and to a theological concept. The part of the Mass that it describes is during the Eucharistic prayer following the Institution Narrative. The Catechism states:
1354 In the anamnesis that follows, the Church calls to mind the Passion, resurrection, and glorious return of Christ Jesus; she presents to the Father the offering of his Son which reconciles us with him.The theological concept at work unlocks what Catholics understand Jesus to mean when he says to "do this in remembrance of me" (Luke 22:19). The USCCB liturgical document "God's Mercy Endures Forever" explains:
Theologically, the Christian concept of anamnesis coincides with the Jewish understanding of zikkaron (memorial reenactment). Applied to the Passover celebration, zikkaron refers to the fact that God's saving deed is not only recalled but actually relived through the ritual meal. The synoptic gospels present Jesus as instituting the Eucharist during a Passover seder celebrated with his followers, giving to it a new and distinctly Christian "memory."So when the Catholic Church refers to the Mass as a sacrifice, she means that is a participation in the one sacrifice of Christ on the Cross through this unique understanding of remembering. Instead of just recalling that Jesus gave his life for our sins like I might try to recall that the Kansas City Royals won the World Series in 1985, the Mass allows me to participate in the Cross of Christ. Applied to my baseball memory, it would be like being able to sit in the stands of the 1985 World Series each time I "remembered" instead of having to settle for poor quality video or someone else recounting the event for me. So just as the merits of the Cross can be applied to me outside of time (since I wasn't alive in 32 A.D.), the Mass allows me to participate in the Cross of Christ outside of time. In this way, the Mass is a "Holy Sacrifice" because it actually is our participation in the one sacrifice of Jesus on the Cross.
It's important to point out how the Catholic notion of the Mass as a "re-presentation" of the one sacrifice of Jesus on the Cross is rooted in our belief in the Real Presence of Christ in the Eucharist. Catholic Answers has a good article that discusses this connection.