Redshift is how scientists understand the rate of universal expansion, and how the universe actually expands in the first place. the expansion of the universe was first theorized by Edwin Hubble.

Scientists had always been curious about whether the universe was really expanding, shrinking, or staying the same. the fact is that with a model like the big bang, It wouldn’t make sense for the universe to not expand or decrease. What scientists did to calculate this, was measure the wavelengths of light received from distant galaxies and nebulae. The wavelength was depicted by the greek alphabet, lambda. lambda looks like this :  λ .

When the wavelength was observed over time, it showed that a vast majority of the galaxies, barring a few (Like Andromeda) had a consistent increase. this means that the wavelengths were becoming longer and longer. lights in the ultraviolet spectrum show that as wavelengths lengthen, they become red. therefore the term redshift was coined. 

The occasional galaxy which was moving toward us was gaining a shorter wavelength. in the UV spectrum, shorter wavelengths have a blue color. therefore as you can deduce, the celestial bodies move closer to us blueshift.