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:
An edge incident to more than two faces.
Two or more faces connected only by a vertex and not by an edge.
Adjacent faces whose normals are pointing in opposite directions.
This video explains these concepts beautifully in Maya.