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!