The Eucharist is Christ really present Body and Blood, together with His Soul and Divinity under the appearance of bread and wine. At Christ's words of consecration offered through the priest, the bread and wine become substantially the Body and Blood of Christ. The Catechism of the Catholic Church reiterates in paragraph 1376 that this change of substance is called transubstantiation. Saint Thomas Aquinas teaches that wherever Christ's risen Body and Blood are, there His soul and divinity are, as well by the principle of concomitance.
After the consecration, the bread changes into Christ's risen Body and the wine changes into Christ's Blood but the appearance of bread and wine remain. Although a person's senses perceive only bread and wine, the Council of Trent (1560) declared that it is "the whole Christ," Who "is truly and substantially" present on the altar. This reality is called the Real Presence of Christ. Eucharistic miracles throughout the centuries have supernaturally manifested Christ's sacred humanity in the Eucharist and are still occurring today.
The Eucharist is one of the seven sacraments but is also called the Blessed Sacrament because it not only imparts the grace of Christ but is itself, Christ. The Eucharist is called the Holy Sacrifice of the Altar, for Christ as high priest offers Himself as the eucharistic Victim to the Eternal Father in atonement for sin. He does this through the ordained priesthood, who act in what's called in persona Christi.
The Eucharist is also called Holy Communion because both priests and laity receive Christ in this manner. Reception of the smallest particle of the consecrated host or the smallest drop of consecrated wine is the actual reception of the entire Christ. The Eucharist is, furthermore, reserved in the tabernacle after Mass, whereby Christ allows Himself to be adored by the faithful. The term Eucharist comes from the word eucharistia meaning to give thanks, which is what Christ did at the Last Supper.
See how Christ is truly among His flock in season one of Church Militant's Premium show, The One True Faith—Eucharist: The Real Presence.