What is double-sided material?
Suppose you want to create a box in Blender and you want to remove one of the faces to show the inside of the box. Although in Blender the cube looks all right (we can see the inner part of the box) in Game Mode, the box looks a bit strange. See the screenshot below:
In order to repair it you have to set all faces of the box to be double-sided.
How to
If you plan to set a face of your mesh to be double-sided, do as follows: select your object and switch to Edit Mode. Switch the selection mode to face selection to easily select faces. The mesh needs to have UV-Mapping flag on. This doesn't mean it needs to have UV-texture applied. The only thing you need to do is to press U key and choose Unwrap. It will create a UV-map for the face, and as a consequence the whole object will get the UV-Mapping flag on.
Now in the Properties Window (see the screenshot below) click on the Object Data icon and scroll down a bit until you'll see the Texture Face section. You can now checkmark Two-side field:
The only thing you have to remember is the fact the Two-side button is available only when the object has UV-mapping on. Moreover if you plan to apply this attribute to all faces of your model you have to do it separately on each face. Selecting many faces at once won't help.
How to debug double-sided materials?
Dark Exporter reports double-sided faces in Blender Console, e.g:
You can see the mesh name is Cube and that only 1 face of that object is double-sided.