A splitter is not found on most production cars, but is a common sight on race cars. This is usually due to the large amount of downforce they can generate on the nose of the car, which would make nearly any car without a rear wing or spoiler unstable or difficult to drive at any considerable speed.
A splitter is a part of the body which sticks out from under the front bumper, and it can often be part of or connected to the underbody. On a normal front bumper, a lot of the incoming air will find its way under the car, which has a number of negative aerodynamic effects. The splitter is designed to "catch" the air that would otherwise flow under the car, and send it either over, around, or through the grille of the car. The splitter itself can be a source of downforce when designed correctly, and the leverage it has (due to its distance from the wheels) multiplies the effect is has on vehicle performance.