Non manifold geometry is when the polygons don't form a continuous surface. - and thus can't be unfolded into a continuous piece. This is relavent when UV mapping and performing certain operations that don't work on non-manifold geometry (for example, boolean operations). Also, some real time engines and other modeling packages don't support non manifold geometry.

Usualy non-manifold means:

*three or more faces share an edge (like when you extrude an edge of a cube)

*Two or more faces share a single vertex but no edge ( like when you merge the corner vertexe's of two planes together)

*adjacent faces have opposite normals (like when you flip the normal of a side of a cube)

Attached is an image to help explain.


Hope this helps!