The roots of the Eucharist are in the Jewish Passover meal. This is the meal which commemorates Israel's delivery from oppression and slavery in Egypt.
As Jesus celebrated the Passover at his last supper with the apostles, He blessed, broke and shared with them bread and wine, declaring that it was His body and blood. He promised that He would truly be with them when they did likewise and shared bread and wine together in memory of Him.
The Mass is the new Passover, with Jesus offering His own body and blood so that we, His present-day followers, might go free. For this reason, as well as being a sacred meal, the Eucharist is also a link with Jesus' death. When we participate in the Mass together with our fellow believers and receive Him in the Eucharist we take part in the Passover meal which He celebrates now, shedding His blood so that we may be saved.