This is the higher-quality type of flat-panel display. It is used for laptop computers and those cool thin monitors we'll all be using some day. In an Active Matrix display, the images on the screen are created by laying diodes over a grid of ultra-small wires. When a current passes through the diodes, they are activated, forming an image.
To keep the diodes in an on or off state, active-matrix displays use transistors. The lower-quality passive-matrix displays rely on the diodes' persistence. The transistors help make the active-matrix displays brighter and give them more contrast. Of course, that also means you're gonna pay more (usually $250-$300 more) for an active-matrix display. But, if you ask me, it's worth it.