What is the substance of bread?
Generically speaking (and, I have to admit, it’s difficult to say this, since philosophers through the ages have debated this topic and come up with a variety of claims!), in the context of the theology of the Church, ‘substance’ can be thought of as ‘being’. That is, it is what makes a thing what it is.
On the face of it, this is a silly definition: when we see something that
looks like a dog, we say “dog!”. However, we need to dig a bit deeper. What would you say that this is:
On the face of it, we would say “bacon and eggs”, right? So, we would presume that this has the “substance of bacon and eggs”. The problem is… it
isn’t bacon and eggs: it’s soap. So, from a philosophical sense, although it
appears to be bacon and eggs, it’s really soap – we would say that its substance is ‘soap’. (In fact, we wouldn’t even say that it has all the
accidents of bacon and eggs, although it has
some (at a surface level, and without deep inspection).)
So, ‘substance’ means “what a thing really is”. Usually “what a thing appears to be” and “what it really is” are one and the same. In the case of the Eucharist, though, we would say that “what the Eucharist appears to be” (i.e., its physical accidents) and “what the Eucharist really is” (i.e., the Real Presence of Christ) are quite different.
Does that help?
(Edited to add:
One last thought, in order to address directly the questions posed by @Spockrates and @clarkgamble1…
In that picture of bacon-and-egg soap, would we say that, at an atomic level, there is the substance of ‘soap’? That is, if we were able to chip off one electron – or even one atom – would we say “this is soap!”…? I think the obvious answer is that we would say, “no, it’s not soap – it’s ‘a proton’ (or ‘an electron’, or ‘a carbon atom’).” In a similar way, then, we wouldn’t say that an electron that strays off a consecrated host is anything but ‘an electron.’
Make sense?)