There are a good many theories about this and nobody knows for sure. There is one popular story, that it derives from the 16 century when France changed to the Gregorian calendar and moved its New Year celebrations from the end of March to the beginning of January. Some people insisted on keeping the old celebration and they were called fools. However, there is no firm evidence for this, and there are examples of people in France using the term 'poisson d'avril' (April fish, the French term for April fool) earlier than the calendar change.

It's equally likely that the custom originates in the ancient Roman festival of laughter, which was held in late March, or the medieval feast of fools, which took place as part of the '12 days of Christmas' celebrations. There are also several folk festivals that involve playing practical jokes, so there may be more than one origin. You can learn more about April Fools' Day traditions here.