How is evidence that stars and groups of stars are moving away from each other relate to the big bang theory

Edwin Hubble's observation of galaxies revealed that the light received from them were red-shifted, indicating that they are moving away from us. And the seemingly farther away a galaxy was, the greater its red-shift. This can only be explained if a all the galaxies were expanding outward. Determining the exact distances to the other galaxies was a problem, however, until the Hubble space telescope. It had high enough resolution to identify Cepheid variable stars in other galaxies, and accurately determine their distance, and therefore the expansion rate of the universe. Hope this helps!!