How did nuclear energy change the world?
A clear question will obtain a clearer answer. Philosophically, the first question is, DID it "Change the world"? Or, was it a part of the continuing changes in the world from its coalescence?
You should have some historical dates/reasons in mind to ask the question. Further, you should distinguish whether you mean to include nuclear weapons (energy release) or primarily useful commercial production of domestic energy from nuclear sources.
The "changes" in lifestyles, attitudes, society and expectations are quite different when attributed to the technology of war and the technology of peace. But in the end, all changes go through the same cycles.
The basic human personality and motivations have not changed for millennia, at least. So, how we as humans deal with, adapt to, or use each change is really the same. The outcomes may be more widespread, or disbursed more quickly. But the impacts are really the same. We improve our life experience, or we don't.