We can learn a lot from animal bones, and jawbones specifically can give us an idea of what an animal ate and how it looked. Three key items in identifying an animal's jawbone are its teeth, its shape and its size.
An animal's teeth determine what it eats. A jawbone with mostly large, pointed teeth likely belonged to a predator of some kind, whereas a jawbone with flat teeth likely belonged to an herbivore, which used those teeth to grind up plant material.
An animal's jawbone has been specialised through centuries of evolution, which makes it an identifying feature. A long jawbone with a gap between the front and rear teeth lends itself well to herbivores, like deer. Carnivores have heavier jaws, designed more for crushing and tearing than browsing.
The relative size of a jawbone correlates directly to the size of an animal. A bear, for example, has a much larger jawbone than a rat, and a much smaller jaw than a blue whale.