What is red shift?
Simplest Answer: the displacement of spectral lines toward longer wavelengths
Definition: Red Shift is a phenomenon connected with light emitted by a source in movement.
More details: Consider a source of light of wavelength
If the source and the observer are at rest then the observer will detect a wavelength
If now the observer is at rest but the source is moving (away from him) with velocity
You can think of it remembering that:
wavelength = velocity x time
In the first case you have:
But in the second case you have velocity=
In normal life (for example, looking at tail lights from a car) you do not detect this phenomenon because the velocity is not very big to influence significantly the detected colour. In case of fast moving object (in space for example) this phenomenon becomes observable.
(hope it is not confusing)