Heh, this being my birthday and having worked with some top astronomers in the past, I can tell you how they explained it: The equinox is when the earth’s equator crosses the ecliptic plane (which is the plane that the earth makes around the sun as it orbits).
In (probably only a little) simpler language, this happens because the earth is tilted like a top relative to the ecliptic plane. For part of the year, the north pole points slightly towards the sun and the south slightly away. Later, it is the other way around.
The equinox is the time when both are pointing at the midpoint of those two extremes, more or less up and down. That means for a brief instant, the equator is parallel to the ecliptic plane.
A good way to see how this works is to get a table and a ball. Mark the ball with a pen or something on the top and bottom. Those will be the poles. Draw a line around the equator between the two poles.
Hold the ball near the edge of the table, which represents the ecliptic plane, so the north pole points a little bit towards the table, pointing over the top of the table. Note the equator is at an angle to the surface of the table.
Now, keep the ball in the same spot, but tilt it so the south pole points at the same angle as the North Pole did, but under the table. The equator will have tilted too.
Somewhere in between those two examples, move the ball so that the equator is parallel to the surface of the table. Note where the North and South poles are now. This is the equinox, and it happens twice a year.
It is those movements of the poles that cause the change in the angle of the equator, and hence the seasons.
The technical term for the way the earth spins on its axis like a top is “precession” in case anyone cares.