The Earth orbits (goes around) the Sun with its axis (the line around which it spins) slightly tilted. This means that in the summer of each hemisphere, that part of the Earth is facing the Sun for longer each day, and so we have long summer days. In the winter, it is the reverse. In between these two extreme times (called the solstices) there are two dates when the Earth is 'sideways on' to the Sun, and then both hemispheres get equal amount of sunlight. These are the equinoxes.

Note the actual date of the equinox varies slightly each year.