Capacitive touchscreens are those that respond to the electrical properties of the human body. This means that they can be controlled by a light touch, and don't require the user to exert heavy pressure on the screen. The drawback to a capacitive touchscreen, though, is that it usually cannot be controlled by a gloved finger or an input device, such as a stylus. There are some input devices that have been optimized for use with capacitive touchscreens, though.
Capacitive touchscreens also are the only ones capable of multi-touch, which allows the display to recognize more than one point of contact. Without multi-touch, you cannot use gestures such as pinching and spreading a screen to zoom in and out.
Apple's iPhone and most Android-based phones feature capacitive touchscreens.