Thankfully, Nintendo is slowly providing some of that information. It looks like AMD will be behind the Wii U's graphics processing, courtesy of a custom AMD Radeon HD GPU. Nintendo and AMD also worked together on the Wii and GameCube, making this latest collaboration not too much of a surprise.
A strong processing backbone is important for the Wii U, which will have to process, and stream information to at least four different screens simultaneously. The console's processor will come from IBM, which wil equip the Wii U with a 45nm multi-core processor with "a lot" of embedded DRAM. (Curiously, a fair bit of IBM's technology was also used in Watson, the supercomputer that bested Jeopardy champions Brad Rutter and Ken Jennings in February.)
Hopefully Nintendo will spill more details in the days to come.