Given the nature of the reform, both in terms of communicating such a fundamental change to a large population and dealing with critics of the new calendar, some Europeans continued to celebrate the new year between March 25 and April 1. April fools were those who still celebrated the holiday in the spring, and were the subject of pranks and ridicule by those who observed the new year months ago.
That's just one theory for the origin of the holiday, however. As HowStuffWorks.com notes on a piece about the holiday's traditions, other occasions resembling April Fools' Day preceded the more contemporary incarnation by centuries.
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Ancient Romans held a festival known as Hilaria. The occasion was used to celebrate the resurrection of the god Attis. Hilaria, of course, resembles the word hilarity in English. The modern equivalent of Hilaria is called Roman Laughing Day.
Other non-Western cultures have their own traditions similar to April Fools' Day as well. In India, Holi, a colorful Hindi festival that frequently entices non-Hindi participants to join in, often is celebrated by people playing jokes and throwing colorful dyes on each other.