Capacitance touch-screen interfaces have been around for a while. They rely on a weak electrical field to register a touch. Here's how they generally work:
Between the glass surface of the Amazon Kindle Fire and the background of the screen is a sandwich of different layers. The base of this sandwich is the LCD display. The layers closest to the screen are conductive layers of transparent material such as indium tin oxide (ITO). These layers create a capacitance grid. The Kindle Fire generates a weak electric field across this capacitance grid.
When your finger -- or any material capable of altering the electric field -- comes into contact with the screen, the field changes. Your finger actually draws current from the field. It's such a weak electric field that you don't sense it yourself. But the Kindle Fire can sense the changes in the field and map them to a specific spot that corresponds to the display screen. The Kindle Fire's software maps the touch to whatever command you were executing.
It's easy to understand with an example. Let's say you want to read your copy of "Fahrenheit 451" by the late Ray Bradbury. You recently purchased the book and so it appears on your home screen. You touch the picture of the book's cover. At that point, the Kindle Fire detects where your finger contacts the screen as the electric field generated across the screen changes. Mapping the location of your touch to the data represented in the icon, the Kindle Fire knows to retrieve and open the copy of the book you've requested.
The grid-like structure of the capacitive screen allows the Kindle Fire to detect multiple touches. The grid creates a series of x and y axes that the Kindle Fire relies upon to determine where you're touching and how many fingers you're using. Earlier capacitive screens in electronics relied on capacitors located at the four corners of a screen, which meant the screen could only deal with a single point of contact.