An apparent change in wavelength of light emitted by something that is moving away from us.
For example, if a star is moving away from us then the light from the star will appear to be red-shifted (in other words, the wavelength of the light is longer than it would normally be). The existence of red shift is evidence that stars are moving away from us - evidence for the Big Bang Theory of the formation of the universe. The larger the red shift, the faster the star is moving and therefore the further away it is.