The V-chip is a small device that administers an electrical shock to an individual whenever they use vulgar language. The device must be surgically placed beneath a patient's skin, where it detects physiological changes in an individual which occur whenever they swear, similar to how a lie detector functions. It can be described as a form of aversion therapy.
In South Park: Bigger, Longer & Uncut, Mothers Against Canada hired Doctor Vosknocker to install a V-chip into Cartman's head to stop him from swearing. It appeared to work perfectly, dissuading Cartman from swearing.
However, the V-chip later malfunctioned after Cartman disabled the electricity for Terrance and Phillip's execution. The V-chip then enabled Cartman to shoot electrical bolts from his fingers, an ability he used to defeat Saddam Hussein.
In the real world, a V-chip refers to any technology which is installed in a television set that allows parents to monitor and censor programs based on their rating.
South Park: The Stick of Truth
The V-Chip reappears in South Park: The Stick of Truth, as an ability called "Curse", used by Cartman where he says dozens of swear words at random before shocking an opponent with electrical bolts. It is very powerful, doing lots of damage and it also uses the most PP of Cartman's moves.