Here's a little "back of the napkin" sketch of the sun's rising points as it marches north and south along the eastern horizon between the two solstices each year.
Imagine yourself high up in the air, looking down upon an obelisk which acts as a gnomon to cast a shadow upon the ground throughout the day as the sun makes its way across the sky. Perhaps you'd like to imagine that your obelisk is the one from the Temple of Karnak in Egypt shown below.
The obelisk in the sketch above looks like a square (because you are looking straight down on it) and it is shaded light blue. The sun will rise over the horizon in the east and move through the sky during the day towards the west (as the earth rotates towards the east, causing objects in the sky to appear to move in the opposite direction, just as a billboard seen from a car will appear to move backwards when the car is driving forwards). The path of the sun is depicted by dotted lines -- the arc of the sun's progress tilts at a slightly different angle each day because the earth is moving around the sun throughout the year, changing the angle we see the sun from our spot on the spinning earth. The shadow of the obelisk is depicted pointing west as the sun rises, one shadow for the summer solstice sunrise and another for the winter solstice sunrise.
Due to the tilt of the earth against the plane of the ecliptic (explained in more detail with more diagrams in the Mathisen Corollary), the position that the sun rises along the eastern horizon will move throughout the year. In the northern hemisphere (the obelisk at Karnak is at 25 degrees north latitude), the axis of the north pole will be most directly tilted towards the sun when the earth is at summer solstice, the point in its path that we call June 21 (our calendar slips a bit from year to year, but the leap years tend to keep our calendar date of June 21 close to the point when the earth is at the summer solstice). The sun will then rise at the most northern point that it ever gets along the eastern horizon (as shown in the diagram above by the most northern dotted arc, labeled "summer solstice").
Conversely, when earth reaches a point at which the north pole is tilted as far away from the sun as it ever gets (at December 21), the sun will rise as far south as it ever rises, and trace a different arc in the sky (shown above and labeled "winter solstice").
These arcs are drawn to depict the fact that the sun makes a much steeper arc through the sky on the summer solstice and a much flatter path on the winter solstice. Another way of describing this would be to imagine that each of these paths of the sun is a paper plate projecting from the flat surface below. The sun would travel along the outer edge of the plate. The summer solstice plate would be much more vertical and the winter solstice plate more horizontal, with its edge much more towards the south. An arrow or a pencil through these plates pointing towards the north pole (around which the entire sky turns) would be pointed much more towards the top of the diagram at the summer solstice and much more towards the viewer of the diagram at the winter solstice.
At the latitude of Karnak (25o north), the summer solstice sun will rise from a position along the horizon such that north will be 64o to the left of an azimuth shot from an observer towards the sun as it peeks over the eastern horizon. By winter solstice, the sun will rise so much further to the south that north will be 116o to the left of an azimuth shot by an observer towards the sun from the same point at Karnak at sunrise.
Back and forth the sun will move through the year, from one solstice to the other, as the earth goes around the sun between the two points on its orbit. Between each solstice, the sun will pass through the equinox position, on the days we call March 21 and September 22 each year. This will be the same point on the horizon because the sun will either pass it on its way north to the summer solstice (in the case of the spring equinox in March) or on its way back south to the winter solstice (in the case of the fall equinox in September). On either of these days, the sun will rise due east, and an observer sighting the sun's rise will know that north is exactly 90o to his left.
As an aside, it may appear that the sun's shadow will draw lines either north or south of the gnomon-obelisk, but in the northern hemisphere above the tropics these shadows will always be to the north of the gnomon. They actually make a curved line in order to accomplish this feat, which you can visualize by thinking about the tilt of the "paper plates" described above. Because the summer solstice arc is very steep, the shadow line will come very close to the gnomon (but always to the north of it) as the sun goes overhead. Conversely, in the winter, when the paper plate is much flatter to the page of our sketch, the line of the shadow will be much further to the north of the gnomon.
The ancients recognized the solstices and equinoxes and paid great attention to them in the alignment of their megalithic monuments and temples. However, they also aligned monuments and temples to dates known as the "cross-quarter days" which are in between the solstices and the equinoxes. These additional dates can be counted off starting from the spring equinox on the way to the summer solstice: the date between the March 21 spring equinox and the June 21 summer solstice is the important cross-quarter date of May 6 (today!). There is evidence that some ancient cultures began their year with this date, and also marked it as the start of summer. In the British Isles this cross-quarter day was called Beltane.
On May 6 at the latitude of Karnak, an observer looking at the sunrise could find north by going 72o to his left. From there, the sun continues its march to the summer solstice position, and then after a pause begins to move back towards the south. Before reaching the equinox position again, it will pass again through the point at which north would be 72o left of the rising sun (where it was on Beltane). It would pass that point around the day our calendars reach August 8th, another cross-quarter day.
From there, the sun would reach the fall or autumnal equinox on September 22, and continue on towards the winter solstice. Before it got there, however, it would pass through another cross-quarter day, on November 8. Now the sun would rise from a point on the horizon from which north would be 108o to the left.
From here, of course, the sun would continue on to the winter solstice. After a short pause, it would turn around again and proceed back to the north. It would pass through position at which north would be left 108o on February 4 or so on our modern calendar. Moving on, it would reach the spring equinox (rising due east again) on March 21, and proceed to the cross-quarter day of Beltane where we started this tour.
In centuries past, important festivals took place on the cross-quarter days, although for simplicity they were moved to the first days of the month (May 1 instead of May 6, or November 1 instead of November 8).
An excellent explanation of the cross-quarter days can be found in Martin Brennan's the Stars and the Stones, which illustrates the alignment of the passage mounds of the Boyne River in Ireland with the sun's rising (and sometimes setting) on different days for different mounds (some equinoctial, some solstitial, and others with cross-quarter days).
The late Barry Fell demonstrated that similar megalithic passages in North America were also aligned with solstices, equinoxes and cross-quarter days in America BC. He argued for the alignment of one megalithic chamber and gnomon in the Mystery Hill (now rebranded as "America's Stonehenge" in a marketing effort) site in New Hampshire with the sun's rise on Beltane, and argued convincingly that the grooves carved at that particular site were an early form of Ogham indicating a dedication to the sun-deity Bel.
There is some evidence, discussed in the Mathisen Corollary, that not all the ancients who established markers and observatories worshiped as deities the heavenly objects they were marking out, but instead were observing them scientifically just as we do today. There is a tension in many ancient writings between those who would worship these heavenly objects and those who worshiped the one who set them all in motion in the first place.
In any event, you now know the astronomical significance of May 6 and the other cross-quarter days.