For Microsoft, the attraction is obvious: money. With the PC, Microsoft gets to sell an operating system: One PC, one OS. With Xbox, Microsoft will receive royalties for every game and accessory. Since most gamers will end up with a small library of games for their Xbox, the equation suddenly becomes one Xbox, multiple royalties. Proof of the console business model can be seen in Sony. Their PlayStation division accounts for about half of Sony's annual revenues. Even the year when Sony's movie division had the blockbusters Men in Black and My Best Friend's Wedding, the PlayStation division brought in more money. When you stop and consider that those two movies have minimal audience overlap, it's hard not to be impressed.
Of course, companies like Sega haven't been as successful. They beat everyone to the gate with Dreamcast, and yet now they've retreated to a software-only position. For the Xbox to challenge the current industry leader, the PlayStation2, Microsoft needed to attract gamers, developers from other consoles, and also from the PC itself. To accomplish this, they would need to put cutting-edge hardware in the hands of the masses. Developers would be attracted to a system with more power to express their creativity, and gamers would flock to the eye candy. Making the Xbox a mass-market device was something Microsoft believed they could do, and for cutting-edge hardware they sought the help of NVIDIA.
For NVIDIA, the attraction of Xbox should also be obvious: money - but some might argue that there's actually a bit more to that. Obviously, NVIDIA has to lookout for its shareholders, and being the exclusive motherboard chipset, graphics chip, and audio chip provider for a product with a $500M marketing budget is certainly a nice position to be in. The reason that PowerVR (Imagination Technologies) continues to be financially strong today is due in no small part to the Dreamcast console and Naomi arcade machines. S3 never recovered from the year between the S3 Virge/GX and the unfairly mistreated Savage3D. After the PowerVR PCX2 of 1997, PowerVR never had a PC chip in the United States again until the Kyro in 2000. (The PC PowerVR Series2 shipped primarily in the UK in late 1999)
What few people know is that the Xbox gives NVIDIA engineers a chance to have some fun by coming back to audio and motherboards, all while sending the bill to someone else. Most people know that NVIDIA's first product also served as a high-quality playback-only sound card with a digital gameport, but did you know that the never released NV2 combined a system chipset, a graphics processor, and audio processor, and everything else with some really wacky glue. The console is familiar territory to NVIDIA.