What is Samhain?

Samhain (pronounced SOW-uhn or SOWN, to rhyme with clown) is the Irish term which is used to describe October 31st or November 1st (or just the month of November).

Literally, the term Samhain means "summer's end" as this was the end of one of two Celtic seasons. The Celts had two seasons, one which ran from approximately May 1st through October 31st and the other which ran from November 1st through April 30th. They had two major holidays which were celebrated at these times. Samhain was both a celebration of the final harvest and a time for mourning one's ancestors. Typically, stories of ancestors would be told while gathered around a fire for meals

While you may be tempted to pronounce the word SAM-hain, this is incorrect. In the Gaelic languages, an h has become the common method to denote lenition, which was represented in the older ogham and uncial alphabets (Uncial is still used on road signs in Ireland and Scotland) by a dot above the letter. This changed the sound of the consonant.
Written in Uncial, Samhain would look something like this: An M with a dot over it would be pronounced as the English W or V, depending on which vowels are before or after it. In Irish, AMHA and ABHA are somewhat abnormal, making an 'ow' sound rather than an 'ahwuh' sound.