Doppler shift of spectral features toward longer wavelengths, indicating recession of the source.
The greater the red shift, the fast the recession. Note that a very strong gravitational force can also produce a red shift. Compare blue shift for example, when a ship is moving away from a star, the star's light appears redder, as the light waves are red shifted, elongated, lengthening the wavelength.
In Terragen civilization, the expansion of the universe was first discovered in presingularity Old Earth, when Edwin Hubble (late Industrial Age Old Earth astronomer) observed that the light from almost all other galaxies was red-shifted.