Similarly to the GameCube (where the graphics component, I/O interfaces and audio capabilities were combined into a single package called 'Flipper'), the Wii follows suit and houses a big chip next to Broadway called Hollywood. In here, we find the graphics subsystem which, to be fair, is identical to Flipper's albeit with minimal corrections.
Thus, Hollywood's GPU still performs the same tasks that Flipper's counterpart did back in the day but now enjoys 1.5x the clock speed (243 MHz). This increase means that more geometry and effects can be processed during the same unit of time.
Functionality
As the 3D engine is still Flipper's, instead of repeating the same pipeline overview, I will mention some interesting design changes that games had to undergo:
Standardised Widescreen
4:3 mode.
16:9 mode, as composed by the video encoder.
16:9 mode, as displayed on a widescreen TV.
GameCube games lacked proper support for widescreen displays (that is, composing 16:9 frames, departing from the traditional 4:3). Nevertheless, Flipper's GPU was already able to do so and a handful of games provided options to activate it, although this was still considered an exclusive feature.
Be as it may, the framebuffer remains identical and the video encoder still outputs a PAL or NTSC-compliant frame, so this 'widescreen' feature is instead accomplished by widening the field of view in the projection matrix. The result is a scene rendered with a larger view angle that now appears squashed horizontally. However, the widescreen TV also plays a part in this process, as it will subsequently stretch the 4:3 frame (coming from the console) and the displayed image will thus look more or less in the correct ratio. If you are curious, this technique is not new, it's been used in film projection and it's referred to as anamorphic widescreen. Also, it's amusing how SNES developers had to deal with the opposite effect.
Back to the point, the Wii standardised this feature by allowing a 'widescreen mode' to be activated from its system settings, which in turn promoted its wide adoption (pun intended).
Screen Interaction
Super Mario Galaxy (2007).
You can pick up the stars by pointing at them.
The new and disruptive controller design meant new types of interactions on Wii games. Since the Wiimote enabled users to point at the screen, some games like Super Mario Galaxy or The Legend of Zelda: Twilight Princess used this feature to allow the player to interact with the scenery.
In the report titled Myth Debugging: Is the Wii More Demanding to Emulate than the GameCube? , developers of the Dolphin emulator explain that games like Super Mario Galaxy and other first-person shooters rely on the embedded z-buffer to identify the object the Wiimote is pointing at and/or check how far the object is from the Wiimote cursor.
This is not a new feature per se, but a novel use of current capabilities. GameCube games didn't depend on a multi-use controller with pointer functionality. Now, players can control the character and point at the screen at the same time.
Updated Designs
The extra megahertz of Broadway and Hollywood, combined with avant-garde designs, brought some improvements to character models. It may not be as significant as other generations, but it's still noticeable and appreciated.
Interactive model available in the modern edition
Super Smash Bros. Melee (2001) for the GC.
4,718 triangles.
Interactive model available in the modern edition
Super Smash Bros. Brawl (2008) for the Wii.
5,455 triangles.
Interactive model available in the modern edition
Sonic DX (2003) for the GC.
1,985 triangles.
Interactive model available in the modern edition
Super Smash Bros. Brawl (2008) for the Wii.
3,644 triangles.
Video Signal
Surprisingly enough, this console doesn't use the old Multi Out port anymore, but a variation of it called AV Multi Out (so much for a name) with a slightly different shape. This one carries all of the previous signals plus YPbPr (known as 'component') . It also includes some data lines that the system uses to identify the type of cable plugged in.
Unfortunately, this medium inherits the same limitations of the GameCube. That is, no S-Video on PAL systems and no RGB on NTSC ones. Also, RGB can only broadcast interlaced signals (no progressive).