Real presence
"Real presence" is the term used to describe the Christian belief that Jesus is in some way present in the Eucharist, the memorial of the Last Supper (also known as Holy Communion and the Lord's Supper).
There are many different views of the Eucharist, ranging from a total transformation of the Eucharistic elements of bread and wine into the body and blood of Jesus (transubstantiation) to a totally symbolic view, found largely in Evangelical, Fundamentalist, and Pentecostal circles.
Specific Eucharistic Doctrines
Catholic Church: the Roman Catholic Church and other Catholic rites believe in transubstantiation, the doctrine that the whole substance of the bread and wine is transformed into the whole substance of Jesus Christ- His body, blood, soul, and divinity. The Church believes that more than a memorial, the Eucharist (and thus the Mass) is a re-presentation of Christ's sacrifice on the Cross.
Anglican Communion: The Anglican Communion officially believes in real presence, though it rejects transubstantiation. Still, some High Church (more liturgical) Anglicans actually accept transubstantiation, and some Low Church (more Evangelical) Anglicans reject real presence altogether.
United Methodist Church: The United Methodist Church beleives in real presence, but rejects transubstantiation, preferring to refer to Christ's presence in the Eucharist as a "Holy Mystery."
Reformed/Presbyterian: Reform and Presbyterian churches generally believe in a "pneumatic" or spiritual presence of Jesus in the Eucharist; while no actual change takes place in the bread, there is still a special closeness to Jesus provided by the Eucharist.
Baptist/Evangelical/Pentecostal/Fundamentalist: While the theologies of these traditions are different, their view on the Eucharist is generally the same- it is simply a symbolic memorial of the Last Supper and a recollection of Christ's body and blood given up on the Cross, but not a re-presentation or literal sharing in His body or blood.