What is a non-manifold mesh

The non-manifold mesh arises while you are editing meshes using tools like Blender. Certain mesh operations cannot be performed on non-manifold meshes. A non-manifold mesh might have one or more elements with the following properties:

1. An edge incident to more than two faces.

2. Two or more faces connected only by a vertex and not by an edge.

3. Adjacent faces whose normals are pointing in opposite directions.

This video explains these concepts beautifully in Maya.