"Therefore, it seems better to say that in the consecration itself, just as the substance of the bread is miraculously converted into the body of Christ so this is miraculously conferred on the accidents: that they subsist which is proper to substance, and, as a consequence, are able to do and to suffer the things which the substance could do and suffer if the substance were present. And so, without a new miracle, they are able to inebriate and to nourish, to be burned and to rot, in the same way and order they would if the substance of the bread and wine were present."  Summa Contra Gentiles BK III ch. 66  

This is in response to a problem regarding generation and corruption:  the sacrament would, in large quantities nourish one and even make one drunk if we are speaking about the wine.  But nourishment is the process of changing some substance, meat or bread, for instance, into my own flesh and blood.  When nourishment happens, are we going to say that its the accidents of bread that are changing into my flesh and blood (since the bread is no longer there), are they nourishing through a miracle over and beyond the substantial change that that happens at the consecration?  

Accidents (quantity, quality, relation, etc..) inhere in substance.  You never see the quality "green" without it being a green something; greenness inheres in a substance - a tree perhaps.  Accidents inhere in substance in a certain order according to St. Thomas and Aristotle.  Quantity is the closest accident to substance.   Quantity inheres in substance and various other accidents inhere in substance in and through quantity.  So St. Thomas holds that in transubstantiation although the substance "what it is" changes, the various accidents remain.  Quantity is miraculously held in existence without a subject in which it inheres.  The other accidents, including all of the various qualities and characteristics of bread and wine, continue to "naturally" inhere in the quantity which is miraculously sustained without a subject.