Doppler effect is defined as a change in observing frequency of a wave, maybe this is too abstract consider: you are sitting next to the river and you suddenly decide to throw a stone in the river, then you notice that the waves around the stone star to increase and grow over one another.guess what? you just cracked the Doppler effect.
The big bang theory can be viewed the same because there was on tiny star(like the small stone) in the universe, that expanded in rippling way until the universe is formed.