Redshift is the lengthening of light waves coming from sources that are moving away from us. If the source is approaching us, came to the opposite effect, blueshift. Light from all galaxies outside the Local Group is shifted to red, indicating that all moving away from us (and from each other). This phenomenon is known as the expansion of the universe.
The redshift was interpreted as a Doppler shift due to removal of the galaxy. The equations for the Doppler effect suggest that a wavelength toward the red and departure speed are proportionate (for speeds much less than the speed of light). Together with Hubble's law we obtain the proportionality between the distance of the galaxy and its speed suspension: the distant galaxy it is, the faster it moves away from us.
Hubble is credited with the discovery of redshift in the spectrum of galaxies (although the phenomenon is actually first notice Vesto Slipher). Hubble, along with Milton Humasonom in 1929th formulated the law of redshift, empirical law between the velocity of the recession of galaxies and their distances, now known as Hubble's law, by which the speed of removal of the galaxy is proportional to its distance. Hubble's law, assuming that the redshift caused by moving galaxies away, consistent with Einstein's equations of general relativity for a homogeneous isotropic universe that expands.