The history of the day has many stories behind it, but as the idea of the celebration itself, you can't know for sure which one or it's true.
In sixteenth-century France, the start of the new year was observed on April first. It was celebrated in much the same way as it is today with parties and dancing into the late hours of the night. Then in 1562, Pope Gregory introduced a new calendar for the Christian world, and the new year fell on January first. There were some people, however, who hadn't heard or didn't believe the change in the date, so they continued to celebrate New Year's Day on April first. Others played tricks on them and called them "April fools."
Today April Fool's day is mostly celebrated by playing tricks and practical jokes on others. The most clever April Fool joke is the one where everyone laughs, especially the person upon whom the joke is played.
Also my paternal grandfather would have been celebrating his birthday today , which I've always found funny, because when he was born, some found it difficult to believe.