The pullup is a closed kinetic chaincalisthenic upperbody exercise that works the Latissimus Dorsi and biceps muscles primarily, as well as several other muscles, such as the midsection. It is considered the gold standard for working the back (for bodyweight). The pullup utilizes a pronated, or overhand, grip, as opposed to the chinup which is similar in nature but utilizes a supinated (underhand) grip.
Kipping Pullups are a variation of the pullup that utilizes the entire body to facilitate the movement, rather than performing them as strictly as possible. A plyometric pullup--one that seeks to increase power--is done by exploding from the bottom of the movement as hard as possible with enough force to perform a clap at the top.