In some ways explaining what bonded leather is can be the same as describing the difference between ground beef and a sirloin steak. The food is all steak, only one is ground up and one is a whole piece. 
Bonded leather is similar whereas you have bonded leather and a full grain leather hide. Bonded leather is leather scraps that are “left over” on the factory floor. These leather scraps are gathered and ground up, then pressed together with a bonding agent to form a “hide”. Thus the name “bonded leather”. Sometimes the process stops here and the bonded leather is 100% leather. Other times the pressed hide is covered in polyurethane that is colored and textured to match a premium hide. This bonded product has much better characteristics than vinyl.
The difference between bonded leather and genuine leather, in terms of quality and looks, can be hard to see. If it is done properly, the grains and textures of bonded leather should look very close to that of genuine leather. In some cases, the only different may be that the texture of the bonded leather may not be quite as pronounced as that of natural-grained genuine leather. The function, smell, and overall appearance can remain much the same, however.
The other major difference with bonded leather is in the cost. It is often available at a substantial discount over genuine leather. This is because the leather scraps, or leather fibers, would have no other value, or very little value, if not made into a bonded form. Therefore, it is still considered a good deal for the manufacturer to sell it at a reduced cost.
One of the most common applications for bonded leather is in the covers for books, especially Bibles. The leather for Bibles can be bonded and still very easily create the desired look and feel. While full disclosure often means the words “bonded leather” appear somewhere on the cover, it would otherwise be hard to tell the difference. It has become such a product of choice for Bibles that finding them in genuine leather is becoming more difficult.