Using draping, the massage therapist only works on the part of the body that is exposed -- your back, one arm or one leg, for instance. The rest of the body is covered.
Most spas use sheets for draping. There may be a throw or blanket that is usually removed before the massage begins, but an electric pads on the table help keep you warm. The room temperature should also be warm enough that you are comfortable.
You usually start face-down for your massage, with your face in a padded cradle that allows you to breath. The therapist pulls back the sheet to work on your back and shoulders. When finished with that area, the therapist covers your back, then uncovers one leg to work on that.
The therapist usually does a quick tuck of the sheet or towel under the thigh, so that they can get to your muscle without any danger of your private parts being exposed,
When it's time to turn over, the therapist holds the sheet or towel up and instruct you to move down so that you are fully on the table, then turn over slowly onto your back. As you're turning, the therapist places the sheet over your body, again, quickly, so you don't feel exposed. This is all considered draping.
A sign of a an experienced massage therapist is that they handle draping in a way that makes you feel safe and comfortable.