Most galaxies appear to be moving away from us. This means that the light from them is "stretched" slightly and appears a bit redder that 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.