Here's why:
* The Doppler Effect: Just like the sound of a siren changes pitch as it moves towards or away from you, the wavelength of light changes as the source moves. If the source moves away, the wavelength stretches, causing it to shift towards the red end of the spectrum (longer wavelengths).
* Cosmological Redshift: Most distant galaxies show redshift, not because they are moving through space in the traditional sense, but because the universe itself is expanding. This expansion stretches the fabric of space, which in turn stretches the wavelengths of light traveling through it.
Important Note: Redshift doesn't just tell us that a galaxy is moving away, it also tells us how fast it's moving away. The larger the redshift, the faster the galaxy is receding. This is a key piece of evidence for the Big Bang theory and the expanding universe.