How does Hubble's Law explain the expansion of the universe?
Hubble's observations of the red shift provided empirical evidence that the universe is expanding. Hubble's law describes how the rate of expansion increases with distance from the observer. This observations do not explain anything, the observations of Hubble's Law, and the red shift require an explanation.
The most common theory that explains the expansion of the Universe observed by Hubble is the Big Bang theory.