Samhain (pronounced "sow-wen," more or less) is the ancient festival that takes its name from the Gaelic "samhuinn," the name for the month of November, originally the first month of the ancient Celtic year. The festival marks the beginning of the winter season and is the ancient Celtic New Year celebration.
The festival came to be a time to honour the dead, especially those who'd passed in the last year, and beliefs evolved that, from sunset to sunset on that day, the veil was thinnest between the worlds of the living and the dead, or that a portal would open, allowing the dead to walk among us.
It's hard to trace the traditions definitively, but it's pretty likely that Samhain is at the core of such diverse observances and holidays as Dia de los Muertos (the Mexican "Day of the Dead" holiday), Halloween, and All Souls' Day.
Comments, clarifications, and corrections welcome. :-)