In 1929, Edwin Hubble discovered that the light from distant galaxies is redshifted, meaning that the wavelength of the light is stretched out and shifted towards the red end of the spectrum. This effect is similar to the change in pitch of a siren as an ambulance passes by - the sound waves are stretched out and the pitch is lowered. Similarly, the light waves from distant galaxies are stretched out due to the expansion of the universe, causing a redshift in their spectra.
Hubble's discovery of the redshift in the spectra of galaxies led him to conclude that the universe is expanding, with galaxies moving away from each other at a rate that increases with their distance. This relationship between the distance of a galaxy and its recession velocity (known as Hubble's law) was later quantified by Hubble and his colleague Milton Humason in 1931.
Hubble's discovery of the expansion of the universe was a fundamental breakthrough in our understanding of the cosmos, and it led to the development of the Big Bang theory, which posits that the universe began as a single point and has been expanding ever since.