Transubstantiation is the Roman Catholic dogma that in the sacrament of the Eucharist (also known as Holy Communion) the bread and wine are transmuted in substance into the Body and Blood of Christ (although retaining the physical "accidents" of bread and wine). This dogma was promulgated early in the Middle Ages in response to scholastics who wanted to know exactly how and in what way the Eucharist became Body and Blood.
Contrast the belief held by most Protestant churches that Holy Communion merely symbolically commemorates Jesus' Last Supper with the disciples; this belief is known as "Symbolism," "Commemoration," or "transignification."
Some churches (notably the Anglican Churches) (others?) profess the doctrine of Consubstantiation, which holds that both the Body and Blood of Christ and the bread and wine are present in substance in the consecrated Eucharist. This doctrine agrees with Transubstantion, and disagrees with Commemoration, that the Real Presence of Christ is in the Eucharist.
The Eastern Orthodox Church teaches simply that the bread and wine become the Body and Blood of Christ, without going into any greater detail than that. Like all the sacraments, it is simply called a "mystery", with the full understanding beyond human comprehension. most Orthodox theologians would prefer to say too little about the details and remain firmly within Holy Tradition, than say too much and possibly deviate from the truth.