Edit 02/26/2016. I am now convinced that resting the beans is necessary. There are just two many roasters I've heard from (on here and in person) that believe it is necessary, and I have seen with my own eyes changes in the appearance of the beans a day after the roast (they seem to darken a bit).
Previously (while still unconvinced). John Snow's and Nathan's answers sound very plausible, but I'm still not convinced that resting fresh-roasted coffee (past the point of cooling) improves its brewed taste. As far as I can tell, no one has ever proven this. DISCLAIMER - I don't want to believe it, because I think brewing after roasting is fun. But I will eventually listen to reason if strong enough arguments present themselves. Below are a couple of points that allow me to remain in disbelief.
There's a guy on YouTube claiming the resting fresh-roasted coffee principle is a myth due to a mistaken case of cause and effect from unskilled coffee shop employees. He goes so far as to tell his own myth of a teenage kid (suffering from acne - nice touch) who sees his employer resting the beans and makes the conclusion that they're better after they sit. But really, the employer is letting the coffee rest because it's impossible to brew large amounts of really fresh roasted (it will explode or something) and the teen is just too lazy to ask. He just wants to smoke weed.
Now if you're not convinced by the explanation above, the only scholarly source I could find is Michael Sivetz's Coffee Processing Technology, Volume 1, where on page 248 he writes,
Beans cannot be ground directly after roasting as they are too soft and would be crushed, flattened, and scarred. When the beans are cool, hard, and brittle, they may be ground.
So I just have to cool them down? Ok, I may be extrapolating a bit since this book is about getting coffee to the masses. And it's very old.
Finally, I'm not a scientist, but I just don't see how carbon dioxide escaping from a bean is going to change the flavor of brewed coffee, especially considering the bean is about to be pulverized and soaked in near boiling water.