May Day is a very old festival, still celebrated in a number of European and American cultures especially. It goes back to the pre-Christian festivals such as Beltane, which was celebrated by the European Celts, and other similar traditions. The main point of these festivals was to herald the arrival of summer - in ancient Rome, for instance, May Day was the festival of Flora, the flower goddess.
Generally May Day nowadays involves dancing, games and other festivities. In some cultures it is celebrated through maypole dancing, which involves dancers, usually children, doing a dance that creates different coloured patterns made with long ribbons.
1 May is also the international labour day or workers' day. Some cultures celebrate both at the same time, while others give more importance to the workers' day and less to the traditional spring festival.
You can learn more about workers' day here and the traditional festival here.