'Red shift' is a key concept for astronomers. The term can be understood literally - the wavelength of the light is stretched, so the light is seen as 'shifted' towards the red part of the spectrum.
Redshift occurs when the light source is moving away from you or when the space between you and the source is stretched. Redshift occurs when the source of light is moving away from the observer. So when astronomers see redshift in the light from a galaxy, they know that the galaxy is moving away from Earth.
