The reason the date is so closely associated with comedy largely has to do with the long-standing feud between the English and the French. Historians claim that on this day in 1789, after the French people deposed King Louis XVI, King George III of England made an historic joke, which continued the tradition to this day.
He pretended to step down.
After renouncing the monarchy the streets were filled with peasants celebrating new-found "freedom." Hundreds were quickly arrested and imprisoned.
It was quite possibly the best prank of all time.
The real history, like many other small holidays, remains a bit clouded in mystery. However, it may have still involved the French.
The likeliest explanation is that it began as a way to mock French people who were slow to switch to the Gregorian Calendar which changed New Year's from April 1 to January 1. These folks were labeled "fools" and some were sent on "fools' errands."
But there are other potential explanations. Others tie it to the Hilaria Festival of ancient Rome, held on March 25, or the Holi celebration in India, which ends on March 31.
The Museum of Hoaxes has a complete collection of all the theories.
Regardless of the history, the day is certainly a time to jest.