Hardibacker Hardibacker - A brand-name tile backerboard that is easier to cut and lighter weight than cement boards. A composite material of cement and cellulose, it's water and mold resistant and secures well with thinset. Hardibacker cannot support itself when used in full sheets and must be screwed in place to a firm backing. For more information on Hardibacker, go to James Hardie's website (manufacturer of Hardibacker). This product is not recommended for exterior or wet locations.
Cement Board Cement board - This is exactly what it says.  It is a cement-based product formed in sheets and reinforced with fiberglass mesh.  It is most often used to construct shower surrounds and as a substrate for tile floors. Cement board is weather and waterproof, permanent, and readily available at your local home improvement center. Cement board is heavy and cannot support itself. It must be screwed in place or to another surface that can support it. When cutting the edge are rough and a bit uneven, you will need to plan for covering or trimming these edges. Thinset should be used as the adhesive when working with cement board. This is not typically a backer that you would use for artwork.  It is better suited for construction or surfacing of walls to prepare for installation. You can create large surfaces to cover building walls etc.  The seams between each sheet need to be taped with alkyd-resistant mesh and filled with thinset prior to applying your mosaic.