I was reading about the doctrine of the Eucharist last night and I realized that many non-Catholics have great difficulty understanding just what the doctrine of transubstantiation teaches. Dave Armstrong gives a nice summary, including the necessary explanation of accidents and substance which are the key to understanding this great mystery.

Transubstantiation is predicated upon the distinction between two sorts of change: accidental and substantial. Accidental change occurs when non-essential outward properties are transformed in some fashion. Thus, water can take on the properties of solidity (ice) and gas (steam), all the while remaining chemically the same. A substantial change, on the other hand, produces something else altogether. An example of this is the metabolism of food, which becomes part of our bodies as a result of chemical and biological processes initiated by digestion. In our everyday experience, a change of substance is always accompanied by a corresponding transition of accidents, or properties.

In the Eucharist—a supernatural transformation—a substantial change occurs without accidental alteration. Thus, the properties of bread and wine continue after consecration, but their essence and substance cease to exist, replaced by the substance of the true and actual Body and Blood of Christ. -- from CHN

A common objection of detractors of the Church is that when the consecrated host is subjected to scientific inquiry, what is observed is no different than bread prior to consecration. This is of no shock to Catholics. As Frank Sheed noted in Theology For Beginners:

One is occasionally startled to find some scientist claiming to have put all the resources of his laboratory into testing the consecrated bread; he announces triumphantly that there is no change whatever, no difference between this and any other bread. We could have told him that, without the aid of any instrument. For all that instruments can do is to make contact with the accidents, and it is part of the doctrine of transubstantiation that the accidents undergo no change whatever. - Theology for Beginners (c) 1981 by Frank J. Sheed, Chapter 18 referenced online at EWTN

A good summary of what the Church teaches regarding doctrine of transubstantiation can be summarized as it is in Ludwig Ott's Fundamentals of Dogma

Christ becomes present in the Sacrament of the Altar by the transformation of the whole substance of the bread into His Body and of the whole substance of the wine into His Blood.

The accidents of bread and wine continue after the change of the substance.

Be careful when discussing this doctrine with others not to insert into it understandings beyond what is taught.