When the siren of an ambulance approaches you, the pitch suddenly drops as it passes by. This is because as the ambulance approaches you, the sound waves are being squeezed together, so you hear a higher pitch. After the ambulance passes by, the sound waves are receding.
This apparent change in the pitch (or frequency) of sound is known as the Doppler shift. Light from distant stars and galaxies can be shifted in the same way. A red shift indicates that a galaxy is moving away from us, while a blue shift indicates that the galaxy is moving towards us.