The simple definition is that they are amazing building materials that anybody can make and use at home with no special equipment or tools.
Now, this doesn't tell you exactly what hypertufa, papercrete and hybridtufa really are, so here is the actual definition and description for each of these amazing building materials.
Hypertufa- Cementitious mix made from peat moss, perlite, vermiculite, and cement. There are probably as many recipes for hypertufa as there are for fruitcake (coincidentally, they are both considered inedible).
Papercrete - Cementitious mix made from paper pulp, sand, gravel, and cement. Basically, papercrete is the same thing as hypertufa but using paper pulp, sand and gravel instead of the peatmoss, perlite and vermiculite commonly used in hypertufa.
Hybridtufa - Cementitious mix made from organic aggregate and a cement binding agent. To put it in context; hypertufa is a type of hybridtufa, but not all hybridtufa is hypertufa. (Example: A typical hypertufa recipe calls for 2 parts peatmoss, one part perlite, one part cement, now let's say that you modify that recipe to 1 part peatmoss, 1 part papercrete, one part perlite and one part cement. Now, you can't really call that hypertufa because it is a hybrid of hypertufa and papercrete - so...you call it hybridtufa).