As with humans, CBD works on dogs because they have an endocannabinoid system (ECS). All vertebrates have an ECS. And we know with humans that the ECS plays a role in pain sensation, inflammation, motor function, and is also responsible for helping your body maintain homeostasis throughout all systems.
The CBD compound is known to be incredibly efficient in terms of these issues. Many of them such as pain, anxiety, loss of appetite, nausea, and inflammation are also shown to have the same benefit on dogs.
However, the research behind CBD and the ECS is just getting started and is still limited. As a result, there is not much medical proof behind those statements, but the positive reactions from dog owners are very promising.