You can perform the towel grip pull-up with an actual towel, a resistance band, or any object that you can hang over a bar and grip. Typically, the towel or other object of choice will be hung right over the bar so that both ends are on either side of the bar. You can grip these ends one in each hand or both in one, with the other on the bar.
When gripping the ends with both hands, this exercise will stimulate the same primary muscles as a close-grip pull-up, but grip strength is at the forefront, along with the latissimus dorsi and rhomboids. When only one hand grips the object, this variation becomes a great way to train for one-arm pull-ups.
The hanging object is more difficult to grip than the bar. Therefore, it leaves much of the pulling work to the side that has a hold on the bar. When training for one-arm pull-ups, you can progress the towel grip variation by moving your hand lower on the towel as you get stronger. This will gradually eliminate the work done by the pulling muscles of the side gripping the towel.
The difficulty of gripping the object makes it easy to compromise form, but full ROM and a neutral spine are still vital with this variation. A standard pull-up bar can be used here, including doorway bars, but the towel or other object needs to be strong enough not to tear or break from the strain of supporting your body weight. A good tip with towels is to fold them once before hanging over the bar to reinforce the fabric.