In medieval times, much of Europe celebrated New Year on the 25 march with a series of festivities which ended on the 1st April. When the new calendar was adopted (1660 in Scotland and not until 1752 in England) it became a source of amusement to laugh at people who continued to celebrate New Year on April 1st or those who simply refused to acknowledge the change. The habit was particularly prevalent in France and it is thought that the custom spread to Britain from France.
Another theory holds that the tradition actually dates back to the pre-Christian era and is related to the Spring Equinox. The European figure of the Lord of Misrule is associated with the Roman winter feast of Saturnalia which evolved into the Feast of Fools which was celebrated (also largely in France) during the Middle Ages. The capriciousness of the weather at this time of year is thought to be reflected in the riotous nature of the pranking associated with this time of year.
The tradition is also governed by a number of superstitions and beliefs. The best known of these is that jokes must be played before noon, or they will rebound on the trickster. Men who marry on April 1st are said to be doomed to be ruled by their wives (ha!), but children born on that date are thought to be simultaneously lucky in all matters except gambling.
Today, the tradition lives on most strongly in the media, who take the opportunity to enliven their programming and front pages with preposterous stories such as the classic 'spaghetti harvest' hoax shown on BBC's Panorama program in 1957.