How does Hubble's Law relate to redshift?
The theory used to determine these very great distances in the universe is based on the discovery by Edwin Hubble that the universe is expanding. In 1929, Edwin Hubble announced that almost all galaxies appeared to be moving away from us.
Astronomers have discovered that in keeping with Hubble theory all distant galaxies are moving away from us and that the farther away they are, the faster they are moving. This recession of galaxies away from us causes the light from these galaxies to be redshifted. This can be ascertained by examining the absorption or emission lines in its spectrum.
These sets of lines are unique for each atomic element and always have the same spacing. When an object in space moves toward or away from us, the absorption or emission lines will be found at different wavelengths than where they would be if the object was not moving (relative to us).