Cosmology
The Fate of the Universe
History of the Universe
Evidence for the Big Bang
Big Bang
Expansion of the Universe

Credit:
When we look at galaxies which are far, far away, we see they are all moving away from us. And, the further away the galaxy is, the faster it is moving. This is happening because the space between the galaxies is stretching.
Redshift
Most galaxies appear to be moving away from us. This means that the light from them is "stretched" slightly and appears a bit redder than it would otherwise do.
This is similar to what happens to sound. Imagine that a fire engine is driving past you with its siren on. When it is moving towards you, the siren it quite high-pitched. When it is moving away from you, the pitch drops, and it sounds lower. With light, "lower" means more red and "higher" means more blue.
Universe

Credit: STSci (HST)