Bits today really mean nothing, hell Bits never really meant anything. The bit is just the word size in binary, and the type of registers involved denote the word length (8bit registers, 16 bit registers etc). The registers are used to store data for quick access functions, such as things dealing with math it needs to crunch.
If it blows your mind that the Gamecube has a 32bit Processor, then how about this. The Playstation 3 is also 32bit, while the Xbox 360 is 64...and people argue that the PS3 is more powerful.
How about this? What was the first 16bit console? Genesis? TG-16? It was actually the Intellivision from Mattel, and the colecovision surpassed it in power, while being an 8 bit system.
What really matters is the processor speed, and overall performance, not so much the type of registers between 32bit and 64bit.