Answer:

The story goes back to the 1500s in France when the Julian calendar (established by Julius Caesar) was replaced with the Gregorian calendar (introduced by Pope Gregory XIII and still used in most parts of the world). In the old Julian calendar, the new year began on April 1, but with the new Gregorian calendar, the new year was set to begin on January 1. News did not always travel fast in those days so not everyone got the word that the start of the New Year changed to January 1. They kept celebrating it on April 1, and they were widely mocked as April Fools. 

The practice of telling April Fools' jokes spread rapidly, and it has continued over the last 500 years or so. These jokes work best on people who have not been paying attention to the calendar. Playing a joke on someone, you want to get to them early in the morning before they realize what day it is.