Without getting to sciency
Wikipedia makes some general statements…
Light roasts - Moderate light brown, but still mottled in appearance. A preferred roast for some specialty roasters, highlights origin characteristics as well as complex acidity.
Dark roasts - Bittersweet flavors are prominent, aromas and flavors of roast become clearly evident. Little, if any, origin character remains.
If you want to go full on science this is a great resource:
http://www.coffeechemistry.com/
Medium-Rare
And to quote a coffee reviewer:
'The analogy of steak works well; people who know steak get it rare to medium-rare–never well done. Well done steak, and heavily roasted coffee eliminate the character of the original, which is why it is rejected by experts of both.'