The common mechanism for creatine supplementation is known to be the increase of intramuscular creatine stores. It is known that CP is used toATP, and that the amount of CP naturally present is well below the maximum amount of CP that the body can store. Increasing dietary creatine allows the maximum amount of CP storage to be reached, which in turn provides more capacity to regenerate ATP.
source: Bodybuilding.com - All About Creatine!
also read this will help you understand ATPs role in muscle contractions.
BIOG 1105-1106 | Cornell Introductory Biology, Individualized Instruction