A huge number of cultures celebrated holidays on the quarters and cross-quarters. Here is a handy 'Wheel of the Year' (this one lists celtic names):
These were distinctive days to early man - the longest day, the longest night, and the days when they were equal, plus those right in between.
Start at the top - the longest night. The world is, for all purposes, dead. It is frozen. The sun has faded to its absolute weakest moment. From that moment on, however, the sun begins to grow again, the world begins to return to life. Many, many cultures thought the sun was male, and had a primary male god being born on the Winter Solstice - the analogy being that the sun is born and begins to grow.
Christmas (Jesus born), Bairn's Birthday, Pryderi's Birthday and the birth of Ra all are supposed to take place around this time, and holidays that take place at the Winter Solstice tend to be celebrations of birth or the return to life. Yule, Mother Night, Christmas, Chanukkah, Saturnalia, others. At the same time, the 'mother' figure (representing the earth itself in many cultures) rests and recovers after the birth - slowly going stronger (nature gains strength beginning with the return of the sun). Note that the one reminder of life to northern peoples on the longest, most frozen night of the year, the one sign that the earth wasn't completely dead, is the evergreen.
Cross quarter - Imbolc - life has begun. The sun-god-child has survived, and will grow strong. Groundhog Day - the holiday is all about saying goodbye to winter, whether you are watching for a creature's shadow, or lighting fires to bring on the spring.
The next major solar event is the Vernal Equinox in the middle of March. Here, the sun-god is becomming a youth, and the earth-goddess has returned to full health and fertility - exactly mirroring what is going on in the natural world. The analogy - a young, strong man and a fertile woman - results in exactly what you would expect - new life. The world bursts out in fertility - spring. Most of the holidays celebrated around this time of year are celebrations of the world returning to life. Fertility celebrations. Ostara, Eostre, Easter (notice any similarities here? Interesting point - the goddess known in the English isles as Ostara and in the north was a fertility goddess. Her symbols were the two symbols of fertility - the egg, and the rabbit.)
Cross quarter - Beltane, May Day - the earth-goddess becomes a woman - a celebration of the reproductive facet of fertility. Fire dances, unmarried women dance around the May Pole (a phallic symbol). The sun-god and earth-goddess are now mates (this isn't incest - is is a figurative representation of natural forces), and the earth-goddess has become pregnant (some say now, some say on the Summer Soldstice.)
Now we have the Summer Solstice - the longest day of the year. The day the sun is in the sky the longest. The sun-god, naturally, is at his most powerful. He is a strong, prime-of-his-life man. Midsummer, Litha, even the Aztec Feast of the Sun. In most cultures, Midsummer is a celebration of
life, of vitality, of human energy. The Christian St. John's Eve is celebrated with bonfires.
Cross quarter - Lughnasa, Lammas, First Harvest
Ok, next comes the Autumnal Equinox. The sun in the sky is shrinking, and the earth is ready for harvesting. This falls somewhere around the middle of September. The sun-god is weakening - he is an old man now, weak and dying. The earth-goddess is an elderly woman - her body (the earth/fertility) is worn out, the fruits of her earlier fertility waiting to be harvested so that she might rest. This is a harvest celebration in most places in the western world. Alban Elfred, Mabon. Expect feasts and celebrations of the bounty of the earth - grains, nuts, meats, fruits. It is a way of saying 'thank you' to the earth for everything it has given. Even though it is a couple of months off, the idea is very similar to Thanksgiving.
Cross quarter - Samhain, Halloween (Hallow e'en, IE Hallowed Evening) - The sun-god dies. The earth-goddess goes into mourning (no more fertility - the earth goes dead). In the natural world, plants die, trees appear to die, animals go into hibernation. The world turns off. This is a celebration of death and the dead. It is thought that the world of the dead and the world of the living are at their closest now, allowing the dead and the living to interact more effectively than ever. People remember their deceased loved ones, light a candle for them. Not too much different from Memorial Day, except everybody is invited. This is, essentially, a memorial service for one's friends and ancestors.
Of course, if the good dead are nearby, then who is to say the bad dead aren't, too? People would put on fearsome masks or carve vegetables into gruesome shapes to frightened off the restless spirits.
Note - some people have called this the celtic New Year. That isn't accurate - this is the end of the year. The New Year isn't until the Winter Solstice. The time in between was just that - a 'between' time, kind of the way dusk and dawn aren't quite day or night. It was just a time to rest and survive.
Finally, we come back to Winter Solstice - and the birth of the sun-god and the earth-goddess coming out of mourning. The paradox, of course, is that this is the same sun-god that impregnated the earth-goddess six months earlier. He is his own father - this myth is actually connected to the idea of reincarnation.
Look at this from the perspective of those that it originated from - the trees die in the fall, then come back to life in the spring. The plants all die, then come back to life, then die again the next fall, then come back to life. The sun (god) weakens and dies in the winter, then comes back the next spring. The earth itself weakens and goes dormant every winter, then comes back every spring. Animals, too, disappear every winter, then come back again in the spring.
The point I am trying to make with all of this is that the picture I posted earlier was called a 'Wheel of the Year', not a timeline. We think of the year as beig laid out in a straight line from January to December - most early peoples thought of the year as being an endlessly repeating cycle, like a rolling wheel. There is no beginning or end - there is just transition to the next quarter or cross-quarter. Just like everything in nature - a cycle of light and dark and ligh, warm and cold and warm, life and death and life.
This example of myth is very, very vague, with no specifics. The specifics changed from land to land (even tribe to tribe), but a very great many cultures have myths and beliefs that fit quite neatly into this template in one variation or another. It isn't coincidence - the longest day, the shortest day, the equal days - these are very, very distinctive times to a people whose only understanding of the world comes through observation.
It is only
natural that most cultures will have an important holiday on the solstices and equinoxes, and that other important events will be placed on the day halfway in between.