This was the same as the start of the Celtic new year, which in Gaelic was called Samhain (pronounced sowin). This came from the Celtic word samonios meaning half, as the dark half of the year was now coming in. Samhain was regarded as starting at nightfall on October 31st. This was called Samhain Night (Gaelic Oiche Shamhna, pronounced eeha howna; the ch is Scottish Gaelic is pronounced as in Bach, while it is usually just pronounced as h in Irish).
This time was regarded by the Celts as dangerous because the dead and beings from the Otherworld were said to be about at this time. While non-pagans no longer regard it as a religious feast, but merely as an excuse for dressing up in scary costumes, it is still so observed by modern pagan groups.
Hallowe'en was popular in Ireland and Scotland and was from those countries exported to the United States, where it enjoys some popularity. Recently, it has migrated from the United States to England, where it is possibly regarded as an American institution by many.
The feast is celebrated in other Celtic areas. Thus in Wales it is called Calan Gaeaf, in Cornwall Kalan Gwaev and in Brittany Kalan Goañv.