I assume that you are talking about the "return to normalcy" that President Harding talked about in the 1920s. I assume this because you have this tagged with "Republican presidents" and because the word "normal" is most connected to this phrase of Harding's.
I have edited the question based on this assumption.
The reason that people wanted to return to normalcy was that there had been some pretty big upheavals in American life in the decades before. The most obvious of these upheavals was the First World War, which had ended just two years before Harding campaigned on the idea of returning to normalcy.
The other big deal was that people had just gone through the Progressive Era with lots of reforms. Harding thought people wanted to just have a rest from all that change.