In a nutshell, LCD is a layer of pixels that let light through or not depending on voltage applied to them, like a digital watch. Each pixel on a plasma display is like a small flourescent tube of gas that becomes illuminated when a voltage is applied.
Plasma is a lot like CRT in that it still uses a phosphorus layer on the screen to create the image (hence they can suffer from screen burn) but rather than use a tube each pixel is made up of three sub-pixels (RGB) which light up when a charge is applied and makes the phosphorus glow.
LCDs have little "shutters" that either allow light through or not (on and off or charge and no charge) and don't rely on a phosphorus coating but a backlight behind the screen.
