The Sacrifice of Melkizedech was a foreshadowing of the Mass.
The Mass is the same Sacrifice as Calvary, presented to us again, but not a repeting of the act, as another sacrifice. To have a sacrifice we have to have certain things happen. The oblation has to be offered to God, and destroyed or consumed. How that happens in the Mass is that the Bread is offered to God, and the priest petitions that it become by God’s power, and the authority given to the priest by his sharing in Christ’s priesthood the body and blood of Christ. Once the elements have become the Body and Blood of Christ, the emolation or consumption of the sacrfice must take place. That is accomplished by the priest’s reception of the elements. Because Jesus Sacrifice is the one true sacrifice that empowers all the sacrifices of the Old Testament as well as obtains all the graces that we receive today, and Jesus is the chief priest at every Mass, it is He who makes each Mass the same sacrifice as Calvary.
In the Old Testament, anything offered to God in sacrifice (Bread, Oil, Flour, an animal etc) was offered to God, and then placed on the altar where the fire would consume some of it, and the priests would consume another part. In many cases part of the animal was given to the person who had arranged to have the sacrifice offered, who would take it home and eat it.