Backerboard

A tile setter mounts colorful American-Olean ceramic tile on a new gypsum backerboard in a motel bathroom...

Source: wiktionary

Ceramic tile has a well-deserved reputation as a durable material, but neither tile, nor cement backerboard, nor latex thinset or grout, can be relied upon to provide waterproofing protection.

Source: wiktionary

There are all sorts of different tile backer board products out there. Some are cement-based, some are gypsum-based, and others have a mix of ingredients.

Source: wiktionary

Dear Tim: What you call backerboard might be something entirely different from what I call backerboard. I'm quite concerned that you don't really have a waterproof backerboard since you said it crumbled. Technically, you have a board that is backing up tile, so I guess you can call it backerboard.

Source: wiktionary