Since a receding galaxy's spectral lines are Doppler shifted to the red, a galaxy's recession velocity is often called its redshift . A galaxy's distance is hard to measure directly, but its redshift is relatively easy to measure from its spectrum. By measuring galaxy spectra, we can map the distribution of galaxies in 3 dimensions. The largest such maps today have about 20,000 galaxies. These maps show that galaxies and clusters lie in enormous sheets and filaments, separated by gigantic voids.
Peculiar velocities affect inferred distance.
We don't know the absolute scale of the maps well, because the value of H is uncertain. General relativity, combined with the cosmological principle, predicts an expanding universe. Doppler shifts show that distant galaxies are receding. Space is expanding. The Hubble constant H is an important number for cosmology, but it's difficult to measure.