The cosmic microwave background (cmb) radiation is a left over of the big bang and the main evidence for the big bang theory:
When the big bang happened, our universe was hot and dense and opaque. There was no matter, only energy. Through expansion and cooling, particles clumped to atoms and the universe became transparent, giving way for the radiation to travel.
The existence of the radiation was forecast through the theory and discovered almost 25 years later in 1964.
More fun at Wikipedia ».