The Holy Eucharist, the Lord's Supper, Holy Communion, Breaking of the Bread all refer to the sacrament commanded by Christ for the continual rememberance of Him.
The bread and wine offered at Communion is the outward and visible sign of this sacramament. It is the Body and Blood of Christ given to his people, and received by faith, that is the inward and spiritual grace. (BCP pg. 859)
On the night he was betrayed he took bread, said the blessing, broke the bread, and gave it to his friends, and said, "Take, eat: This is my Body, which is given for you. Do this for the rememberance of me."
After supper he took the cup of wine, gave thanks, and said, "Drink this, all of you: This is my Blood of the new Covenant, which is shed for you and for many for the forgiveness of sins. Whenever you drink it, do this for the rememberance of me."
Remembering now his works of redemption, and offering to you this sacrifice of thanksgiving.
(Eucharist Prayer C, BCP pg. 371)
An interesting note: there is a significant difference between the way Protestant Churches and the Catholic Church view the Holy Eucharist, and this goes to why non-Catholics are not allowed to receive Communion at Catholic Mass and Catholics, in turn, choose not to recieve the Eucharist outside of the Catholic Church. Catholics believe in transubstantiation - the bread and wine actually become Jesus. For Protestants, Epsicopalians among them, they are symbolic of Christ's body and blood, not the real thing.