The GameCube GPU is a complex, tight-knit piece of hardware with impressive features for its time. It is so powerful and so flexible, it was used unmodified within the Wii architecture. For a comparison, just imagine a SNES running with an NES's graphics system. This is completely unheard of, before or since. The GameCube is a remarkable achievement of hardware engineering! With its impressive capabilities, emulating the GameCube's GPU has been one of the most challenging tasks Dolphin has ever faced.
As well as games work, developing proper emulation of the GC/Wii GPU continues to be an ongoing and difficult process. Dolphin has had long standing issues with a bunch of its features, and many graphics glitches have been around for years and years. With the merger of the tev_fixes_new branch (tev = Texture EnVironment, a major component of the GameCube's pixel processing pipeline), Dolphin's emulation of the GameCube GPU is going to the next level.