The amount of sunlight (daylight) earth receives is directly related to the tilt of the earth's imaginary rotation axis. The tilt of the earth is 23.5°. During the time of summer in the northern hemisphere, the tilt of the earth faces more towards the sun, and the sunlight is directly incident on it. So, the amount of daylight (or the duration of the day) is higher in summer.
On the other hand, during winter, the tilt of the sun faces opposite to the sun, so it receives a lesser amount of daylight, and so is cold during this time.
