A corporeal thing is a thing having physical substance. The Latin word 'corpus' means 'body', and thus corporeal means, loosely, that something 'has a body'.
So, corporeal things have bodies that can be touched, have mass, occupy space, are otherwise tangible.
Incorporeal things are those that seem to exist but can not actually be touched, have no mass, and otherwise are only real in the sense that they appear to be real in an illusory way.
An example of a corporeal being is a normal person standing in front of you that you can hug.
An example of an incorporeal being is the tooth fairy - an imaginary being that can be visualized, spoken to, etc., but not actually touched.
Note: the term corporal has related meanings, but much different usage and connotation. For example corporal punishment, literally punishment of the body, refers to physical acts of spanking, flogging, whipping, or even capital punishment. One could not interchangeably say "corporeal punishment."
The Latin root for both words, corpus (body) is also the root of modern English words like corps (a group of people) and corpse (a dead body). The term corpus is also sometimes used in English to a body of related facts or objects, as in "a corpus of knowledge" and British National Corpus.
