Road handlebars are referred to as 'drop bars', so yes, 'riding in the drops' means putting your hands down on the bottom. 'On the hoods' means up on top of the brake/shifters, and 'on the tops' means your hands are on the flat part of the bar.

Shifting your hands and riding position help alleviate some overuse problems. Riding in the drops is a more aero position, and used in sprints and descending. I use it just to stretch out my back on long rides.