From an Orthodox and Catholic perspective, the bread and wine in the Lord's Supper are believed to become the actual body and blood of Jesus Christ through a mystical transformation. This transformation is understood to be a result of the priest's consecration during the celebration of the sacrament. Believers hold that they are receiving the body and blood of Jesus in a real and tangible way, as a source of grace and spiritual nourishment. This belief is considered a central aspect of the sacrament, and is seen as a way to participate in the sacrifice of Jesus on the cross and to be united with him and with the community of believers.
As a former Lutheran, Lutherans would also argue for a Real Presence of the body and blood of Christ "with, in, and under" the bread and wine. These are two quotes from the Formula of Concord - Epitome
1 Although the Zwinglian teachers are not to be reckoned among the theologians who affiliate with [acknowledge and profess] the Augsburg Confession, as they separated from them at the very time when this Confession was presented, nevertheless, since they are intruding themselves [into their...
bookofconcord.org
2. We believe, teach, and confess that the words of the testament of Christ are not to be understood otherwise than as they read, according to the letter, so that the bread does not signify the absent body and the wine the absent blood of Christ, but that, on account of the sacramental union, they [the bread and wine] are truly the body and blood of Christ.
6. We believe, teach, and confess that the body and blood of Christ are received with the bread and wine, not only spiritually by faith, but also orally; yet not in a Capernaitic, but in a supernatural, heavenly mode, because of the sacramental union; as the words of Christ clearly show, when Christ gives direction to take, eat, and drink, as was also done by the apostles; for it is written Mark 14:23: And they all drank of it. St. Paul likewise says, 1 Cor. 10:16: The bread which we break, is it not the communion of the body of Christ? that is: He who eats this bread eats the body of Christ, which also the chief ancient teachers of the Church, Chrysostom, Cyprian, Leo I, Gregory, Ambrose, Augustine, unanimously testify.