On a drop (or racing or road) handlebar, the different parts of the bar have names. The flat part near the stem and headset is the "flats". The gently sloping part on top of the curve is the "hoods". And the curvy bit where you can reach the brakes easily is the "drops". Most bikes are set up so you can brake some from the hoods, but it's harder.

(to go with drop bars, you'll also see people talking about shifters. Brifters are shift levers stacked with brake levers. Bar end shifters are stuck in the holes at the bottom ends of drop bars. And stem or downtube shifters are little shift levers that aren't on the bars at all.)

And Teawoman, I'm glad you're mostly ok. The idea of falling on a hill really scares me, since that's the one time it's easy for a bike to go fast.