The Clean Power Plan is central, but not essential, to the United States' role in global climate action. Obama's success in climate climate diplomacy is notable; whether he earned the Nobel Peace Prize when he won it or not, he probably has now. His leadership abroad was by all accounts integral to the international passage of the Paris Agreement, and in 2016 he threw the country's weight squarely behind bilateral deals that brought China and India towards joining as well.
The Paris Agreement is a framework for moving ahead global action on climate change. Once it is ratified by an international quorum, all 191 signatories to the Agreement become party to its rules, which include mandated emissions cuts by each state. It's up to the country to say how it will achieve those emissions reductions, and the Clean Power Plan is Obama's signature policy behind America's intended contribution.
Necessary context: The Clean Power Plan is important, but it's not enough on its own to reach America's target.