What role does the strong force play in the structure of an atom?
It binds the nucleus together.
The atom consists of electrons outside a positively charged nucleus. The nucleus, in turn, consists of protons which are positively charged, and neutrons, which are electrically neutral - and together they are called nucleons. The electrical forces of repulsion between the protons confined within the extremely tiny nucleus is enormous, and without some other binding force to keep them together, the nucleus would have simply flown apart! It is the strong nuclear force between the nucleons that binds the nucleus against this repulsion.