Seriously or you're joking? Sorry, not quite sure STI levers are the type of integrated road road levers that have brake and lever and shifter in one mechanism, often called brifters:

http://en.wikipedia.org/wiki/Sti_shifters

Hood is the soft plastic/rubbery hood over the top of the road levers. So "on the hoods" means your palms resting on those hoods, as opposed to "on the drops" or "on the tops" of the bar. That's the position usually required to operate the shifters.