Why do we have shorter and longer daylight hours?

The variation in daylight hours or duration of daylight hours is due to the tilt of Earth on its axis and Earth's revolution around the Sun. The Earth rotates on its own axis once every 24 hours, which is the duration of a day. This axis, which runs from the North Pole to the South Pole, is tilted at an angle of about 23.5 degrees with respect to the plane of orbit of Earth around the Sun. In the northern hemisphere, during the summer months, the axis is tilted towards the Sun and hence the northern hemisphere experiences longer daylight hours. In winter months, the north pole (and hence the axis) is tilted away from the Sun and hence, we have shorter daylight hours in northern hemisphere. 

A similar phenomenon is observed in southern hemisphere. It experiences summer when northern hemisphere is experiencing winter. However, southern hemisphere too experiences longer daylight hours during summer months. 

Hope this helps.