How does the Earth's tilt and movement cause the seasons?
The north-south pole axis sits 23.5 degrees off the solar plane.
The solar plane is the plane stretching out from the sun's equator through the solar system. And relative to that plane the earth tilts at 93.5 degrees. When the northern hemisphere experiences the 1st day of summer, the solar plane is cutting through the Earth at 23.5 degrees north of the equator.
When the southern hemisphere experiences summer, the northern hemisphere experiences the sun's rays at 47 degrees off the solar plane, a very indirect angle. Therefore, winter.
Since the Earth is in constant motion around the sun, the exact location of the solar plane upon the earth is also in constant motion, therefore we have the ever changing seasons.