Riding in your drops will decrease your wind resistance.
Up to 80 percent of the resistance you encounter on the bike comes from aerodynamic drag. Reducing this wind resistance is a key factor in increasing speed.
The more upright your riding position, the more aerodynamic drag you create. By lowering your torso towards the top tube, you essentially "get under the wind" by reducing your aerodynamic profile.
If you're a recreational rider and speed isn't a major concern, then comfort should be your primary consideration. But if you're a competitive cyclist looking for ways to get faster, gradually adjust your riding position to make yourself more aerodynamically efficient.
The Trade Off
There are, however, sacrifices to comfort and perhaps power when you make adjustments to your riding position. These have to be balanced with the decreased drag the new position creates. Initially, you'll probably lose a little power as you adjust, but after you're used to the new position you should gain a subsequent increase in speed.
Aero bars, as favored by triathletes and time trialists, significantly reduce drag but require a different fit and frame type than traditional road bike geometry. Simply bolting on a pair of aero bars won't help you unless you can produce power comfortably in this position. You'll need the right bicycle and a professional fit to get the full benefit from aero bars.
Making the Change
It's important to make small changes in your riding position over time versus large adjustments. If a new position is painful or causes an overuse injury, reverse it immediately.
If you spend most of your time in the hoods (on top of the brake levers), a good place to start is by switching to a lower hand position (drops) for short periods of time. Start off with as little as five minutes and progressively increase the amount of time you spend in the drops. Eventually, you should spend a majority of your time here unless you're climbing a steep grade.
Once you're comfortable in the drops, you can lower your stem height. Lowering your stem height decreases the angle at your torso. Stem height can vary from zero to four inches below the height of the saddle. When you lower your stem height, there'll be less aerodynamic drag from your upper body, but power and climbing ability will be reduced. Lower the stem in small increments and let your body adjust to the new position.
Remember, the faster you get the more the air around you slows you down. If you can ride consistently over 20 mph, an aerodynamically-efficient riding position should be a primary objective. The type of riding you do should also be considered. Generally, the more time you spend in the saddle during your goal events the more of a priority comfort should be.