Question

What does the red shift suggest about the universe?

Answer 1

So far, the only way we know to explain the red shift is
as an effect of the light sources moving away from us. 
That's the basis of the whole idea of the expanding universe,
and ultimately, the big bang theory. 

If we ever find another mechanism that can produce the same
shift in the wavelengths of light without the source moving away
from us, then the whole system of the expanding universe and the
big bang theory will fall apart.