There are considered to be three distinct types of redshift: doppler, cosmological and gravitational.
Doppler shift is the change in wavelength of electromagnetic radioation through movement between the source and observer. If the cource and observer are becoming closer, the wavelengths become shorter and hence shifted towards the blue end of the spectrum (blueshift); if they are becoming further apart, the wavelengths become longer and hence shifted towards the red end of the spectrum (redshift).
A similar effect occurs with sound waves from, say, the siren of a passing ambulance. As the siren approaches it sounds higher in pitch (blueshift); as it recedes it sounds lower (redshift).
Cosmological redshift is observed in the electromagnetic radioation from distant objects such as galaxies and quasars, and is a result of the expansion of spacetime between the source and observer during its time of travel.
Gravitational redshift results when electromagnetic radiation travels against a gravitational field, for example the light leaving a massive star. Since the speed of light is constant, when it loses energy in the gravitational field its wavelength increases and hence is redshifted.
Written for Sue 1999-09-20