I don’t want to restate everything that Ari wrote in his excellent post, but I think he missed some crucial elements in explaining its origins.
The Jewish Calendar year, like several others, is based upon three independent variables: the sun, the moon, and the vegetative cycle. Holidays will generally be located in reference to at least two, if not all, of these variables. Additionally, there is a trend toward ‘shoehorning’ lunar phenomena into solar ones, if for nothing but convention.
For example, Pesach begins at the full-moon – a lunar phenomenon, after the vernal equinox – a solar phenomenon, and if it had been determined that the rains had ended and the barley harvest ready to begin – a vegetative phenomenon (though linked to the solar year).
The solar year is punctuated by two major phenomena, subdivided into four, and then eight days which are naturally predisposed to being holidays. The first two are the solstices, the equinoxes are the midpoints between the solstices and also identifiable in their own right, and the four midpoints between the solstices and equinoxes. Most major ancient holidays are based on these subdivisions; it’s not an invention of modern Wiccans and neo-Pagans.
It is convenient to use these solar phenomena and holidays to mark the beginning, middle, or end of a (generally vegetative) season. Thus, in the Gregorian Calendar, we use the equinoxes and solstices to mark the beginning of each season. In other calendar systems, they were used to mark the midpoint of a season. Thus, as is familiar from Shakespeare and Tolkien, the ‘Midsummer’ holiday actually takes place at the time of the summer solstice, on or around June 21. The Chinese and Japanese calendars follow this type of system as well. In those systems, the midpoints between the solstices and equinoxes are the dates upon which the seasons begin or end.
In the Jewish Calendar, since months are lunar, no dates ever exactly correspond to solar phenomena on a consistent basis. Nevertheless, a lunar date can roughly correspond to a solar phenomenon. Thus, the four seasons (tekufot) are named for the months during which they generally begin – Tishrei, Tevet, Nissan, and Tammuz. In a two-season year, such as the one that the Mishnah uses (the ‘rainy’ season and the ‘sunny’ season), those seasons would start at the equinoxes and reach their midpoints at the solstices. The Biblical festivals are, without exception, determined by the occurrence of the equinoxes.
Another aspect of ancient lunar or lunisolar calendars is the tendency to have holidays at full moons. There’s light, it’s easy to identify, and the moon rises as the sun sets. Also, if the month begins with the moon’s first appearance, it allows for the timing of the holiday to be announced, as there was generally some uncertainty associated with the timing of the moon’s first appearance. That’s why Rosh Hashana, the lone Biblical holiday which is indeterminate even after the day begins, is observed for two days everywhere.
In the standard Jewish calendar, therefore, there are four ‘yemei tekufah’ – equinoxes and solstices – which VERY ROUGHLY correspond to the first days of the month of Tishrei, Tevet, Nissan, and Tammuz. Of those dates, three of the four are commemorated as significant dates (the First of Tevet always corresponds with Chanukah; see also Avodah Zarah 2a, which describes the origins of Saturnalia. 1 Nissan is the beginning of the year in most Biblical accountings, and see Mishna Rosh Hashana 1:1). Furthermore, Pesach and Sukkot are also rooted in the turning of the season around the time of the equinoxes, but begin at the full moon.
There also are four ‘midseason’ dates, each of which occurs on a full moon (since they lie 1.5 months after the beginning of the season). They are: 15 Cheshvan, 15 Shevat, 15 Iyar, and 15 Av. Once again, three of the four are significant dates on the Jewish calendar (15th of Iyar is ‘Pesach Sheni’). The 15th of Shevat is recognized as the midpoint of the winter, much as Groundhog’s Day is recognized as such in America. The 15th of Av would be recognized as the midpoint of the summer, or ‘Midsummer Day’ when the season begins at the equinox. The Celtic festival of Lammas or Lughnasadh corresponds to Tu B’Av. In the Mediterranean, it would have been linked to something related to agricultural cycles, in this case, the beginning of the grape-harvest.
Since the Jewish Calendar is so rooted in the Land of Israel (which we tend to lose sight of outside of the Land), as is the very religious rhythm of the Torah, and since there are natural ‘highlights’ in this rhythm, it’s important to keep those elements in clear vision when trying to understand those holidays.