If binding energy is responsible for holding nucleons together than what is meaning of strong force?
Whenever there is a force, of any kind, there can be energy associated with what the force does. For example, if the force is attractive then it can hold two things together. In this case to pull the things apart you would have to apply a counter-force, and as the things moved apart, pulled by such a counter-force, energy is being supplied. The total amount of energy that would be required is given by multiplying the force at each stage by the next small amount of distance moved by the body the force is acting on, and then adding up all these contributions. The total is called binding energy.
In the case of nucleons the force is the one called "strong nuclear force" and the energy required to pull the nucleons apart is called their binding energy. These are two aspects of the same physical effect.
There are examples in other areas. For example, molecules are held together by electromagnetic forces, and the energy required to separate them is again called binding energy.