What did Edwin Hubble's 1929 measurements of distant galaxies' redshift show?

Answer

More distant galaxies are moving away faster, a relationship now called Hubble's law.

Context

In 1929 Edwin Hubble combined distances to nearby galaxies, which he estimated from Cepheid variable stars, with their velocities from the redshift of their light, which Vesto Slipher and others had measured. He found that the farther away a galaxy was, the faster it appeared to move away, a relation now written v = H0 × d. Belgian physicist Georges Lemaître had derived and estimated the same relation two years earlier, and the International Astronomical Union renamed it the Hubble-Lemaître law in 2018.

The key reading is that the galaxies are not flying outward through space from a center. Space itself is stretching, which carries distant galaxies apart and stretches light waves on their way to us, producing the redshift. Every observer sees the same pattern, so there is no special center. Gravitationally bound systems such as the Milky Way and Andromeda do not expand along with it.

Hubble's own value of the constant, around 500 kilometres per second per megaparsec, was much too high because of errors in his distance scale; modern values are roughly 67 to 73. Running the expansion backward gives an age of about 13 to 14 billion years. The disagreement between measurement methods, known as the Hubble tension, is still unresolved.