I'm surprised this hasn't been mentioned... But road bike tires are thinner, with bigger diameter. Thinner = less rotational inertia and better acceleration (easy to maintain speed). Bigger diameter = you cover more road with the same stroke.

Yes, mountain bikes are a lot heavier, but I think the more important reason why road bikes are generally faster is because of the wheels, particularly the rear wheel.

Also, the low profile of the road bikes help a lot with drag. a LOT