According to Garderian, Alexandrian, and traditional lore Samhain is a time when the Veil that separates the world of the living and the world of the dead becomes thinner, allowing spirits and other supernatural entities to pass between the worlds to socialize with humans. It is also the time of the year when Ancestors and other departed souls are honoured and entreated for luck and prosperity.
In parts of western Brittany, Samhain is still heralded by the baking of kornigou; cakes baked in the shape of antlers to commemorate the god of winter shedding his cuckold horns as he returns to his kingdom in the Otherworld. The Romans identified Samhain with their own feast of the dead, the Feast of the Lemures or Lemuria. This was observed in the days leading up to May 13. With the coming of the Christians the festival in November (not the Roman festival in May) became All Saints' Day or All Hallows' Day on 1st November followed by All Souls Day or All Souls' Day on 2nd November. The night of 31st October came to be called All Hallow's Eve and the remnants festival dedicated to the dead became known as Halloween.
The Gaulish calendar may have divided the year into two halves, the 'dark' half, beginning with the month Samonios (the October/November lunation), and the 'light half', beginning with the Giamonios (the April/May lunation). The entire year appears to have been considered as beginning with the dark half, so that the beginning of Samonios may be considered the Celtic New Year's day. All months began at full moon, and the celebration of New Year took place during the 'three nights of Samonios' or trinux, the full moon of nearest the midpoint between the autumnal equinox and the winter solstice.
The full moons marking the middle of each half-year may also have been specific festivals, the Coligny calendar marks the mid-summer one, as Lughnasadh, but omits the mid-winter one, Imboc.
The seasons are not directly linked to the solar year, the solstice and equinox but the midsummer festival was considerably later than the summer solstice, around 1st August. It appears that the calendar was designed to align the lunations with the agricultural cycle of vegetation, and that the actual movements of the Sun were less important.
In medieval Ireland, ''samain'' remained the principal festival, celebrated with a great assembly at the royal court in the Hill of Tara, lasting for three days, consistent with the Gaulish testimony.
The popular literature over the last century or so has given birth to the near universal assumption that Samhain, now associated with Halloween, was the Celtic New Year. This is now being disputed.
In Stations of the Sun' (Oxford University Press, 1996), the historian Ronald Hutton points out that there are no references earlier than the 18th century in either church or civic records that suggest this was true. It is generally correct to say that Samhain is Summers End. With the end comes a new beginning.
The etymology of the word is complex: Samhain' is from the Old Irish samain, samuin, samfuin, referring to lathe na samna', samhain day, on 1st November, and the festival and royal assembly at that date in medieval Ireland ('oenaig na samna, samhain night). It is often known as summers end, and spelt with an 'f'' that suggests 'sam' summer and 'fuin' sunset or end. The Old Irish 'sam' is summer, in Welsh it may be 'haf' in Breton' 'hañv', in Old Norse 'sumar' all meaning "summer", and finally in Sanskrit there is 'sáma' for season.
Another links is in Prot-Celtic which has 'samani' meaning an assembly, in Sanskrit there's sámana', in Gothic samana (and incidentally in Catalan semana, but that's an aside).
So Samhain may not refer to summer at all but to an assembly, although the word is derived from words meaning summer – confused, so are we. If you need more look at Wikipedia