A documentary filmmaker went to Harvard’s 1987 graduation ceremony and asked the students this question. Only two out of 23 were able to give a correct explanation. I like to draw the following lesson from the story: education often doesn’t give us scientific outlook.
Sun shines with equal power throughout the year. Yet, it doesn’t mean that the intensity on the surface of the earth is also same throughout the year. To understand this, consider the following analogy.
Imagine that a spherical ball is spinning along its axis in the vertical direction. Imagine a light bulb few meters away from the ball. The light of the bulb falls normally in the equatorial region of the ball. But, it falls tangentially in the regions near the poles. Hence, the equator will be brighter, and hotter, than the poles.
What happens if the axis of rotation of the ball is not vertical but inclined towards the bulb? Now, the northern hemisphere of the ball tilts towards the bulb. So, in the northern hemisphere of the ball, most of the light rays hit almost normally. In the southern hemisphere of the ball, most of the light rays will hit only tangentially. This makes the northern hemisphere hotter than the southern hemisphere.
Now, suppose the ball starts revolving around the bulb on a circular path in such a way that its rotation axis is transported parallel to itself. After the half revolution in the circular orbit, the southern hemisphere of the ball tilts toward the bulb. Hence, it is hotter than the northern hemisphere.
The earth is like the tilted ball and the bulb is like the Sun. It takes one year for the earth to complete one revolution around the Sun in a nearly circular orbit. For half of the revolution from the vernal equinox, the northern hemisphere tilts towards the Sun. This is the time when there is summer in the northern hemisphere and winter in the southern hemisphere. For the other half of revolution, it is the other way around.
[Answer to a question on Quora]