What it is
Nipple pulling or tugging involves using either the fingers or something like a nipple clamp to grab the nipple and pull on it. A firm grip does not necessarily equate to pain, though tightening the grip (i.e., pinching) or pulling strongly can hurt. There are a number of situations where simply pulling or tugging on nipples can be effective.
Physical control by nipple
A dominant or top may firmly grasp their partner's nipple or nipples to lead them around. In the absence of a leash---or even when one is available---leading your partner by their nipple can be a powerful expression of control or ownership. Also, if your partner happens to be kneeling and you want them on their feet, grabbing their nipple and pulling upwards can be a quick and satisfying way to get them to stand.
Nipples and predicament bondage
Nipples can be useful attachment points for some styles of predicament bondage. For example, when you lay your naked partner on their back beneath a pulley, tie their ankles together either directly with rope or with a spreader bar, and then run a rope from their ankles or the bar over the pulley you can pull their ankles up thus exposing their genitals and butt.
If you then attach the end of the rope to a pair of clamps attached to their nipples you have your partner in a very challenging situation. When they lower their legs to try and rest them this pulls painfully on their nipples. When they keep their ankles up to relieve the tension on their nipples then their legs get tired. All the while you get to play with their pink bits while they suffer. See the illustration on the right.
Nipple pulling and sensation play
Because pulling on nipples doesn't necessarily cause pain we can also classify this activity as a type of sensation play. It can range from gentle pulling, kneading or twisting using your fingers, to something more mechanical such as the use of nipple weights which apply a constant downward pull on the nipples.
Nipple weights are perhaps most effective when the submissive is bent over forwards allowing the weights to hang down freely. When at the limits of the submissive's tolerance much fun can be had when the dominant then swings the weights back and forth. Bondage can be usefully added to keep a submissive bent over such as by standing them up, tying their wrists together behind their back, and then running a rope from their wrists over a pulley attached to the ceiling.