How is Solstice and Equinox related to the position of Earth's axis?

Answer 1

JLynes's answer is pretty good, except that winter solstice is minimum angle, summer solstice is maximum angle.

The equinoxes are the points at which day and night are of equal length--about half way between the soltices.

Answer 2

They're related to the angle of the axis in relation to the sun. At the solstice, both winter and summer, the axis is inclined to its maximum relative angle*, creating the longest and shortest days of the year. At the equinox, the axis is inclined to its lowest relative angle, crossing the celestial equator and creating equal day and night.

*Edit after Natanovich's entry: I should have said "maximum relative angle from the vertical". Still, it's the maximum relative angle either + or -, depending on which hemisphere you're in.

Answer 3

None