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.