Though there are other theories of organization, when working within the theory of systems, the definition of organizational behavior is that "organizational behavior is a term applied to the systematic study of the behavior of individuals within work groups" (Chaneta, "Organizational Behavior"). So you may have your question turned around a bit.
It seems to me you are asking how to show the value of the definition of a term to the term. The answer to this is that the value of the definition to the term is that the term and its definition are inseparable: one exists because of and in the other. Perhaps what you are really asking is how to prove that the definition as it stands is a valid one, a valuable one. That also is difficult to answer because it asks a thing to prove what it is from within itself; proofs are easier to make working from what is external to the thing being proved, otherwise your result may be that it proves it is itself because it is itself.
Having said all this, one way to approach what I think you want to know is to consider what organizational behavior would be comprised of if not by systematic study of the components of the organization. There is no substitute for systematic study of the components within the organization that can evaluate what comprises organizational behavior. Thus systematic study of the components of the organization is valuable to organizational behavior since they are integrally united. Organizational behavior is the systematic study of the "principal issues addressed by organizational behavior," which are:
• Individual behavior and performance at work;
• The nature and working of people in groups;
• The nature of social structures and organization design at work;
• The processes involved in adapting behavior to meet changing conditions. (Chaneta, "Organizational Behavior")
Systemic study is very important to organizational behavior because you need to understand how all of the pieces of your organization are inter-related and the effect each has on the others. Often a company will make a change without looking at how that change will affect the rest of the business. This can be very detrimental.
A system looks at the formal and informal structure of a business, as well as the physical environment, the individual, and how they interact.
Each part is essential. None can exist alone in the system. This system approach is the basis for modem organizational theory, which is founded on behavioral science studies. (enotes)
The key is ensuring that no piece of the puzzle gets overlooked. Nothing in your organization exists in a vacuum.
This would be sort of difficult to do, I think. This is because you would have to do a systematic study first (which takes time and effort) before you could show that the study has any value.
I suppose that one thing that you could do would be to conduct a systematic study of an issue that affects your particular business. Then you could show people higher up in your company that the conclusions drawn from the study can show them how they should get your firm to behave. In other words, they would have some suggestions that are based in actual results from other firms instead of simply having to go based on their gut.