A diagram showing how the Sun moves through the sky on an equinox. Click on image for full size (50K GIF)

The upper panel shows that on an equinox (which occurs around March and September 21), neither half of the Earth points directly towards the Sun. In fact, the Sun is at the equator, so both halves of the Earth are getting about the same amount of sunlight. For you in Topeka, the altitude of the Sun is about 50°, in between its altitude on the solstices. The bottom panel shows how this looks to someone standing on the ground in Topeka.

Equinox literally means "equal night". On the vernal (spring) and autumnal (fall) equinoxes, day and night are the same length. Neither hemisphere gets more sunlight than the other, so both have similar seasons (fall in one hemisphere and spring in the other).

How high the Sun gets in your sky, and how long it is above the horizon during the day, depend not only on the season, but also on your latitude.