How does Hubble's Law resolve Olbers Paradox?
Hubble's Law shows that the more distant a galaxy higher is its red-shift. So the visible light from galaxies that are too far away would be red-shifted to invisible wavelengths. So stars beyond a certain depth of space would go invisible resolving the Olber's Paradox .
Olber's Paradox: It occurred to Wilhelm Olbers that if the Universe is static, eternal and infinite in extent (that was the prevailing notion back then) then one would expect to see the sky to be extremely bright. Because in whichever direction you look, your line of sight would end in a star. So the entire sky should be extremely bright and luminous without any gap of darkness.
But what we observe is a dark sky with points of light (stars). This discrepancy between expectation and observation is called Olber's Paradox.
How does Hubble's law resolve Olber's Paradox?:
Hubble found that light from distant galaxies are red-shifted. The farther a galaxy is from earth, higher is its red-shift. A linear relationship between red-shift and distance means that light from objects that are beyond a certain depth would have all its visible light (and other shorter wavelengths) redshifted to invisible part of the spectrum.
Even if the Universe is infinite in extent stars beyond a certain depth will remain invisible and from visibility perspective it is as though they are non-existent. This is how Hubble's law resolves the Olber's paradox.