This behavior is primarily because the earth's axis is tilted.
The earth revolves around the sun and completes one revolution each year, This causes various seasons. The earth is tilted on its axis, and in summer in the northern hemisphere, the northern hemisphere is tilted toward the sun. This makes the days longer, but more importantly, the suns rays hit the earth in the northern hemisphere more directly and therefore are more intense. This makes it warmer.
When it's summer in the northern hemisphere, the southern hemisphere is tilted away from the summer, and it is winter there.During the summer, the sun's rays hit the Earth at a steep angle. The light does not spread out as much, thus increasing the amount of energy hitting any given spot. Also, the long daylight hours allow the Earth plenty of time to reach warm temperatures. During the winter, the sun's rays hit the Earth at a shallow angle. These rays are more spread out, which minimizes the amount of energy that hits any given spot. Also, the long nights and short days prevent the Earth from warming up.