Background
In Mac OS X 10.1, nearly all graphics appearing on a screen were a product of Quartz. Quartz was the underlying graphics system, which allowed OS X to have translucent menus, throbbing blue buttons, anti-aliased fonts, and all sorts of Aqua-y goodness.
Problem
Nearly all of the computations required to draw graphics were performed by the CPU. Unfortunately, a CPU is not really designed to do the computations required to draw graphics. The heavy load, in some situations, made OS X slighly sluggish while the CPU figured out how to draw everything pretty-like.
Solution
Announced as a new feature of Mac OS 10.2 (“Jaguar”), Quartz Extreme is an overhaul of Quartz. The most notable thing about Quartz Extreme is that, assuming you have a compatible graphics card*, the calculations needed to render the desktop (a three-dimensional scene with textures) are handled by the GPU**. Along with a number of other small tweaks, Quartz Extreme is perhaps the single most important technology responsible for speeding up OS X.
Apple's symbol for Quartz Extreme is a two-color Q, silver and dark blue.
*Apple recommends a graphics card with 32 MB of VRAM; however, it should be noted that the newer iBooks (which have 16 MB cards) CAN take advantage of QE.
** For those with a more technical background, this load-shifting is accomplished by pipelining Quartz through OpenGL to the GPU.