SAMHAIN - 31st October
Halloween has a celtic origin: it was celebrated especially in the celtic parts of Britain and France. There, it was called Samhain, which literally means "the end of the summer". In fact, this day was the end of a celtic season because it was time to harvest the previously grown crops and to decide which animals to kill to have food during the winter.
The Celts believed that the veil between dead and people alive was at its thinnest, so the souls of the dead people came to their respective homes to mingle with their families. In order to please these spirits and ward off the bad ones, Celtic people left some food and candies outside their houses (that's where the current "trick or treat" comes from). Furthermore, people used to disguise (normally with animal heads and skins) to protect themselves from bad spirits and lit candles to guide their relatives' soul home, usually inside turnips. Bonfires were also established as a cleansing method and herders use to walk between two bonfires with their cattle (especially in Scotland). It was also an appropriate night for divination. The most popular divination method was to drop egg whites into water and foretell the future based on the shapes.
When Christianity arrived on these islands, there was an attempt to turn this celtic festival into a religious one, because celts were supposed to worship the Devil, even if this evil character never existed in the Celtic culture. That's how this festival became an important religious day (All Saints' Day) and the night before was called All Hallows' Eve (hence Halloween). The Irish emigration to North America during the 17th century was the reason why all these customs arrived in the USA. Over time, instead of turnips, they started to use pumpkins, much bigger and easier to hollow out.
This picture shows a turnip carved by Irish people celebrating Samhain in the 20th century.
http://www.bosquemingshu.com/eventos/samhain/samhain.html
http://en.wikipedia.org/wiki/Samhain
http://arquehistoria.com/historias-origen-de-halloween-samhain-y-los-celtas-592
http://www.bbc.co.uk/religion/religions/paganism/holydays/samhain.shtml