This is an explanation I found on the internet and it makes sense.
Manifold is a geometric topology term that means: To allow disjoint lumps to exist in a single logical body. Non-Manifold then means: All disjoint lumps must be their own logical body. Of course that definition is often more confusing so perhaps the best way to think of Manifold and Non-Manifold is this: Manifold essentially means "Manufacturable" and Non-Manifold means "Non-manufacturable". In other words manifold means: You could machine the shape out of a single block of metal....and with a non-manifold shape you could not.
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Also, Kerry, excellent description for the manifold bodies. That is a hard one to describe.