This isn't just a regional or even Western thing; in the Eastern Church, where he is more commonly known as St John the Forerunner (maybe that would be good for those thinking his customary Western name makes it seem like he was a Baptist in the denominational sense), his birth is also celebrated on 24 June, and has a vigil and an afterfeast the day after.
So why 24 June? Well, the details come only from St Luke, who says that when Gabriel announced to Mary she would bear the Messiah if she agreed, that her cousin Elisabeth was already six months pregnant. But hey, if Jesus' birthday is celebrated 25 December, shouldn't it be 25 June?
In our calendar yes, but they didn't have our calendar. In the Roman Imperial calendar, days of one month were counted backwards from the first, called the kalends, from which our word calendar comes btw, of the next month. Christmas is eight days before the kalends of January, so St John's birthday was put eight days before the kalends of July, but, due to our present Germanic way of counting days now, that makes it fall on 24 June.
No-body, btw, supposes these are the actual birthdays of either Jesus or John, but only that it puts them correctly relative to each other.
Either way, it puts the Nativity of St John around the time of the Summer Solstice. Some suppose that therefore this feast is just a Christian cultural appropriation of the solstice from pagan culture in the process of evangelisation. Not likely, since the feast is centuries old and in the Julian calendar that was in use in mediaeval Europe until 1582 the Summer solstice is earlier, in mid-June! Not to mention the date of the feast of St John is calculated from when Jesus' birth is celebrated, not the Summer solstice.
Nonetheless the coincidence with the approximate time of the solstice is clear and did have influence. Though people had no idea it was because of the tilt of the Earth's axis toward or away from the Sun, they could see that daylight hours in a day increased and decreased through the year. The Summer Solstice is the so-called longest day of the year; while all days have 24 hours it has the most sunlight hours, and sunlight hours begin to decrease until the Winter Solstice or so-called shortest day of the year with the fewest sunlight hours.
In pre-Christian Europe, the beginning of shorter daylight during the day was marked in many and varied ways, the common element being bonfires. Why bonfires? The idea was, that with more and more darkness during the day, evil spirits and/or other not so well-intentioned factors may move about more easily, so light was lit to ward them off. Bonfires, and the jumping over thereof, are still a feature in northern European countries.
The Christian version of all that has more to do with the relation of St John to Christ. Right after the feast of the Nativity of St John the Baptist, sunlight hours begin to decrease, even as John said of Jesus "He must increase and I must decrease" (John 3:30). Many period documents reflect the tension between earlier non-Christian observances of solstice with the Christian observance of the birth of St John.
The Summer solstice is still called Midsummer (Sommersonnenwende in German, gotta throw that in) from its solstice observances. One of Shakespeare's most popular and enduring plays, A Midsummer Night's Dream, is named from it. The play is loosely based on antics from Ovid's Metamorphoses (Publius Ovidius Naso, Books of Transformations, 8 A.D.), ending with the suggestion that it's all a dream. It may have been written for Queen Elizabeth I in celebration of the feast of the Nativity of St John, though there is no conclusive documentation of that.
In between the two solstices are the two equinoxes, with about equal daylight and dark hours, and these four formed the Quarter Days, the four days marking the turn of the seasons. In the olden times in Mother England, the Quarter Days were when rents were due, worker contracts were made, and magistrates had to complete tours of even the most outlying areas of their jurisdictions to assure that none went unduly long without a hearing and resolution. Justice delayed is justice denied, as we say.
This last was one of the provisions the barons got from King John in the Magna Carta on 15 June 1215. The Magna Carta, meaning Great Charter in English, was the first time that subjects -- though these subjects were themselves local ruling land owners, barons, the original "free men" (in German, Freiherren) -- got from a king certain rights and limitations of royal power as a matter of law.
This set in motion a development of rule of law rather than a king's or ruler's will, one of whose descendants is the Constitution of the United States. 2015 was the 800 year anniversary of the Magna Carta. We shouldn't be so surprised that the rule of law doesn't always take so well, as if it just takes naturally, when we try to export it to other places. Have they been working this out for 800 years?
The "Robin Hood" movie of 2010 takes its context in the beginning of this development, specifically, the Carta de Foresta, or Charter of the Forest, of 1217, hammered out after numerous violations of the 1215 document. In fact it was with this charter that the first charter of 1215 began to be distinguished as the magna carta, or great charter. The Magna Carta version of 1297, which includes amendments, is still part of English law.
The Quarter Days are:
25 March. Called Lady Day, also known as the Feast of the Annunciation, and until 1752, New Years Day. In Mother England 6 April is still tax day, which you may hear echoed in our 15 April. Hold on, wasn't that 25 March? Calendar change, remember -- 25 March in the old Julian calendar became 6 April in the now current Gregorian one.
24 June. The Nativity of St John the Baptist, also known as Midsummer Day, with reference to the Summer Solstice.
29 September. Michaelmas, the mass on the Feast of St Michael the Archangel, for which this blog (as with all the Quarter Days, actually) posts.
25 December. Christmas, the mass on the Feast of the Nativity of Jesus.
Saints are usually commemorated in the church calendar on the day of their death, that being the day of their birth into eternity, but Jesus, his mother Mary, and St John the Forerunner are the only three whose births into this life are also commemorated.
So lots to celebrate -- John, and even more importantly his whole significance, Jesus whose forerunner he was; the development of our present form of governance; Summer and all the daylight and warmth! And a really cool movie to see!
And may you have a pleasant, uh, Midsummer Night's dream too!