Dragging your brakes is applying them lightly. On downhills you do this to slow yourself while still maintaining directional control. If you merely lock them up, you're sliding and not able to steer (as well).
In general, braking should be done and completed just prioring to entering a turn. Use both brakes. As you get ready to apply the brakes, you should shift your weight rearward (to keep from going over the bars if you apply too much front brake). As you enter the turn, you should release the brakes and move your weight forward to apply more weight to the front wheel so that it will bite better to initiate the turn.
Dragging the brake through a turn is an advanced technique that can be better explained by Ol89'r.
Learn to use both brakes. Your most stopping power comes from your front brake. Practice using the front brake only. Find a flat, smooth area with a predictable surface and practice coming to a complete stop using only the front brake.
Only use one or two fingers on the lever. This way, if you start to lock up the front wheel you can release the lever while still gripping the bar. If you use all of your fingers on the brake lever, you will be unable to release the brake lever if you start to go down. Be sure to wear all of your riding gear since you may hit the dirt a couple of times while learning to do this.
Once you are comfortable with using only the front brake, start applying both brakes evenly. The more you get used to using the front brake the faster you will be able to go. It all comes with practice.
Dragging the brake is usually done with the rear brake to stabilize you while you are in a turn. If you slightly apply the rear brake in a rough turn and drag it, it will help you hold your line better in the turn and keep the rear end of the bike from jumping around. Also, going down hill dragging the brake will help keep you stable but there again, most of your stopping is done with the front brake.