Edwin Hubble's groundbreaking discovery was the observation of a linear relationship between the distance to a galaxy and its redshift. This relationship, known as Hubble's Law, is a fundamental principle in cosmology.

Here's the breakdown:

* Redshift: Light from distant galaxies is shifted towards the red end of the spectrum. This is a consequence of the Doppler effect, where the light waves are stretched as the galaxy moves away from us.

* Distance: Hubble used Cepheid variable stars, which have a predictable relationship between their brightness and pulsation period, to determine the distances to galaxies.

* The Relationship: Hubble found that the farther away a galaxy was, the greater its redshift. This means that galaxies are moving away from us at a rate proportional to their distance.

This discovery led to the following conclusions:

* The Universe is Expanding: The observed redshift of distant galaxies indicates that the Universe is not static, but expanding outward.

* Hubble Constant: The proportionality between distance and redshift is quantified by the Hubble Constant (H₀), which represents the rate of expansion of the Universe.

Hubble's Law has profound implications for our understanding of the Universe, leading to the Big Bang theory, the age of the Universe, and the evolution of cosmic structures.