Harder wood (maple) - brighter tone
Dense wood (mahogany) - warmer tone
That's really the jist of it.
Fundamentally, it's a matter of physics. How vibrations are transferred and conducted by the wood. Tighter more compact wood grains will transfer vibrations at a higher frequency and give a brighter tone. More dense wood with not so compact grain patterns will transfer vibration at a lower frequency (bleeding off some of the high end) and will give a warmer tone profile.