The Catholic doctrine which states that the wafers and wine one ingests as part of the ritual of communion is actually the body and blood of Jesus Christ. Transubstantiation holds that the material used in the communion ritual is not merely a symbol for the body and blood of Christ, but that it literally becomes such at the moment the priest says "This is my body" in the Eucharistic Prayer.  Obviously, the wafers and wine do not change in outward appearance. Not all Catholics accept the doctrine and many others do not give the concept much thought.
"Christ is present whole and entire in each of the species [of bread and wine] and whole and entire in each of their parts, in such a way that the breaking of the bread does not divide Christ."
- — Catechism of the Catholic Church 
The doctrine of transubstantiation is generally rejected by protestants. The orthodox church features a variety of views that are similar, but not identical to, transubstantiation.
No evidence of transformation
There is no physical evidence the wafers and wine are transformed.
Consumption of human flesh and blood is cannibalism. This accusation traces back to at least the time of Pliny the Younger (c. AD 110). Catholic apologists reject this argument saying that consuming the living body of Jesus is fundamentally different from consuming a dead non-divine human.