What did Hubble's observations show the universe is doing?

Hubble's observations showed that the universe is expanding. In 1929, Edwin Hubble published evidence that more distant galaxies generally have larger redshifts, indicating they are receding from us faster than nearer galaxies.

Hubble combined galaxy-distance estimates, based partly on Cepheid variable stars, with redshift measurements from astronomers including Vesto Slipher and Milton Humason. The resulting distance–velocity relationship became known as Hubble's law. It showed that space itself is expanding on large scales, rather than galaxies simply moving through an otherwise static universe.

A common mix-up is saying that Hubble discovered the Big Bang outright. His observations established cosmic expansion, while theoretical work by Alexander Friedmann and Georges Lemaître had already explored expanding-universe models. Modern observations further show that expansion is accelerating, a result associated with dark energy and discovered through studies of distant supernovae.

The expansion does not mean that every object is flying away from every other object locally. Gravity keeps systems such as the Solar System, the Milky Way, and the Local Group bound together; expansion becomes evident across much larger distances.