I'm lumping samhain and the hunters moon together in one post this year as they have come in the same week and close enough to affect each other.
The hunters moon came first on October 29th, I call it the hunters moon but I have also heard of it called the drying grass moon and the travel moon.
The hunters moon is named so because around this time people would be hunting to build their stores full of meat for the winter.
Oddly enough if you skip to Samhain, Samhain was also a time to slaughter and prepare for the winter (or maybe not odd?), Samhain falls on October 31st through November 1st though I have heard of people celebrating it October 25 through to November the 5th.
Samhain is also celebrated as the death night for the old year (the witches new year I've heard it called)
Samhain was often used for good celebration as well, people can and would tell fortunes about the coming year as well as some cultures bobbing for apples believing that the first apple caught would signify the first person to be married that year.
Samhain was/is also a time where spirits and ancestors from one's past can cross the veil and visit. People often leave out supper, or in the case of a serve yourself feist an empty plate would be left so the spirit could serve themself.
But just as a happy ancestor can come through the veil so can a murderer or other undesirable spirit so people must be careful. But hey that's where carving turnips came from. people use to carve turnip lanterns to light the way outside and to ward against malicious spirits. More commonly used now is the pumpkin which I am thankful for because turnips are hard to carve.
There are other stories about the carved turnip involving malicious fairies and also how people would leave food outside to gain the fairies favor for the upcoming year, but I don't know much more about that. I suggest any fairy work be researched elsewhere because I'm pretty clueless about fairies.
But here's a lantern for your enjoyment courtesy of wikipedia.