Why are clear nights colder than cloudy nights ?

Explanation

On a clear night, the earth radiates energy into space at a rate proportional to the fourth power of its temperature (about 300 K). The incoming radiation from space is very small because its average temperature is near absolute zero. On the other hand with cloud over, the earth radiates at 300 K, but the radiation is absorbed in the clouds, which radiate energy back to earth again the radiation is trapped, like the green house effect.