The expansion of the universe has also been compared to the inflation of a balloon. Suppose that before you inflate the balloon, you draw dots on the surface of the balloon to represent different galaxies. After inflating the balloon, what observation would you expect to make?

That the universe (the balloon for this case) is expanding and that is the reason why the galaxies (the dots) appear to move away one from another.

Explanation:

By means of looking at the spectra of galaxies, it can confirm that they are moving away in an accelerated motion.  

Spectral lines will be shifted to the blue part of the spectrum if the source of the observed light is moving toward the observer, or to the red part of the spectrum when it is moving away from the observer (that is known as the Doppler effect). The source in this particular case is represented for each of the galaxies.      

Hence, the redshift represents this shift of the spectral lines to red part in the spectrum of a galaxy or any object which is moving away. That is a direct confirmation of how the universe is in an expanding accelerated motion.

The redshift can be define in analitic way by trought the doppler velocity:

 (1)      

Where is the wavelength shift, is the wavelength at rest, v is the velocity of the source and c is the speed of light.

(2)

Where z is the redshift.      

The ballon example, once that it is inflating, represents how is the universe which it is expanding and that is the reason why the galaxies (the dots) appear to move away one from another.