In the early twentieth century, President Warren Harding popularized the word normalcy with his slogan: “return to normalcy," about getting back to normal life after the war. Since then, the word has been used often instead of "normality."
Normalcy, pronounced "NOR-mal-see," is a state of being normal, usual, or expected. When something returns to a state of normalcy, it is returning to the way that it ought to be. It is another word for normality. Some people believe that normalcy should not be used because the word normality is more formally correct, but in the U.S., you'll often see normalcy used. When it comes to choosing one, take your pick.