A cosmological redshift is a shift in the wavelength of received light from distant objects such that the wavelength of the light we are seeing is LONGER than the wavelength of the light that was emitted by the object we are looking at. This is like hearing the siren of a fire truck shift to a lower pitch as it moves away from us, HOWEVER, the cosmological 'red shift' has nothing to do with motion as we normally experience it. Instead, Einstein's general theory of relativity says it is caused by the expansion of space between the time the light was emitted, and the time it was received by us.