The Holy Eucharist is the official name of the worship service each Sunday. It is also known as Holy Communion, the Mass, or the Lord's Supper. But we use the ancient term Eucharist.
It comes from a Greek word meaning to "give thanks", and because it is a thanksgiving service, it reminds us over and over again that we can be grateful for God's gift to us of life, and God's gift to us of salvation in Jesus Christ, and God's gift to us of this sacrament so that we can be nourished by Christ, made one with Christ and with each other, and carry that thanksgiving and unity and Christ-identity with us into the world.
The World Council of Churches' document Baptism, Eucharist and Ministry is an ecumenical document that describes very broadly what Christians believe happens in these sacraments. Also the Catechism in the Book of Common Prayer describes our Episcopal understanding of the Eucharist.