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I believe the way that it works is because less total IR energy is entering the greenhouse of the car. Some of it is simply absorbed, but some of that is radiated out to the outside air rather than the inside, which is where all of it would have gone without the tint. And some of it is reflected from the tint; even ones that just "look dark" will reflect some IR radiation. (And visible light as well.)
As to quantifiable effects, I do not have any numbers. There is a significant amount of anecdotal evidence, but we all know how reliable that can be.
Still, I intend to have it done (professionally) on my car at some point.
-soD
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