If a wave source is moving relative to an observer there will be a change in the observed wavelength and frequency. This is known as the Doppler effect.
The wave source could be light, sound or microwaves.
When the source moves away from the observer, the observed wavelength increases and the frequency decreases.
When the source moves towards the observer, the observed wavelength decreases and frequency increases.
There is an observed increase in the wavelength of light from most distant galaxies. The further away the galaxies are, the faster they are moving, and the bigger the observed increase in wavelength. This effect is called red-shift.
The observed red-shift provides evidence that the universe is expanding and supports the 'Big Band' theory (that the universe began from a very small initial point)
Cosmic Microwave Background Radiation (CMBR) is a form of electromagnetic radiation filling the universe. I comes from radiation that was present shorty after the beginning of the universe.
CMBR existence can currently only be explained by the 'Big Bang' theory.