Red shift occurs when the source of radiation is moving AWAY from you. The radiation might be sound or light or any other electro-magnetic radiation. The classic example is a train whistle. When the train approaches, the whistle has a higher pitch than when the train is stationary, and a lower pitch when the train recedes.
Astronomers use measurements of the red shift of stars and galaxies as a distance indicator.
If you would like to know more about how that works, please ask in another question. Ph. D., Division Director.