Regular 3D Rendering
Conventional Wisdom says:
The conventional approach to 3D graphics involves triangles and what is known as the Z-buffer. In this method, each triangle is described by x,y, and z values. A 3D chip starts in the distant back and draws all the triangles for that Z-value. Then, when the chip is done with all those triangles, it starts drawing everything at the next Z-value, which covers up part of the layers behind it. This process is repeated over and over until the chip finally reaches the camera and is very similar to painting pictures on a canvas, one on top of another, over and over. Let's take a look at a screenshot from the Dreamcast:
Example from Shenmue
With a conventional 3D architecture, the sky is drawn in its entirety first, then a few mountains, then a few skyscrapers, then a few more, a plane, and finally the village that's closest to the camera. The problem with this approach is that a lot of time is wasted drawing things the viewer would never see. About half of the sky is being covered up as well as the skyscrapers that are being covered up.
The PowerVR architecture
The PowerVR chip used in the Dreamcast looks at the whole scene, or more accurately at tiles that divide up the screen. The chip check pixel by pixel to see which polygons are closest to the camera (and hence the only one the viewer sees) and then renders the tile all at once. The trick is that the PowerVR is only drawing what the viewer can see so time isn't being wasted. In the above example, the PowerVR would be drawing exactly what you see; the sky would only be drawn where it can be seen. If half of the sky that normally would be rendered is not, and about a full screen's worth of mountains and buildings is not drawn either, then the PowerVR has just saved one and half screen passes (overdraw), or 1.5 * 100 = 150 MPixels/sec. Voila!
Your effective fillrate is now 250 MPixels/sec. In other words, you'd need a regular 3D card with a fill rate of 250 MPixels/sec for the same performance. Whereas a busy city scene would tax even the best of 3D cards, the PowerVR has a much easier time since it'd be only drawing the buildings the person can see. So while 1 gigapixel/sec is a bit excessive, the PowerVR is a very competitive part.
Not too much overdraw here
but still at 60fps
Since developers are fully aware of this feature, you can expect many developers to take advantage of the Dreamcast unique rendering approach with more complex scenes and environments. Remember, console developers don't have to worry about hundreds or thousands of different system configurations, and so it's easy to push everything to the limit.