I have discussed the IaaS and PaaS benefits in many threads before, but find that many still are still hesitant about the computational effectiveness of the Azure cloud. Gamers have been left out of the loop, the Azure cloud and even the Xbox one implementation has not been really covered on anything other than straight tech sites.Rather than spoon-feed, I'm going to go straight into using cloud processing/storage directly from the Xbox one. Many of you are only here for Halo. ctrl+f if that's all you are interested in, no judging.

tl;dr Microsoft revolutionized the way developers access cloud computing resources. This is revolutionizing the world, and we get it in our freaking game console. Microsoft provides the Common Language Runtime to facilitate easy programming for Windows. It handles the complex and sticky stuff such as managing execution of the program, memory management, type safety and exception handling. It worried, mostly, about resources on the local machine -- CPU, RAM, etc. Until now, there was no equivalent for easily executing and divvying up operations to cloud resources. Rolling your own code to do this is cost-prohibitive and not worth it for nearly any company to develop. The only reason it is for MS is because it will be integrated into over 90% of the home computers in the world, not including enterprise and mobile systemsMicrosoft changed the game by introducing a new model, a CLR equivalent, for their Azure cloud.

tl;dr The new system is called Orleans and it makes accessing cloud computing storage and processing power just as straight-forward as local resources. Microsoft's new cloud programming model is called Orleans and has been in development for a few years. It organizes units of computation and storage as "grains" that can seemlessly migrate between datacenters. It ensures consistency and replication. It manages debugging, performance monitoring, deployment, configuration and maintenance. It's simple(incredibly important). It uses .NET languages which are easy enough to teach an elementary school kid in a week, yet robust enough to have developed some of the world's most complex enterprise software. Source Source 2 Visual Models: 1, 2, 3

Also, Halo

"The cloud-systems team celebrated a year of successful deployment of its distributed cloud technology—Orleans—in production for Microsoft’s Halo team, and the team has scaled its system very significantly since then."

Halo is being developed for the cloud, and they haven't even told gamers yet and have been for at least a year and a half now. Shh. This was reported to ZDNet months ago. Titanfall has already confirmed the use of cloud resources in rendering and AI.

Tech analysts report of effects

That processing power enables things like instantaneous Kinect Source

Artificial intelligence, [..]doesn’t need to be calculated for every single frame of the game. Your enemy in a game will close in on you, but it only needs to know where you are every second, rather than every split second. So that task can be offloaded to the slower connection to the servers. Source

Some rendering, like trees in the distance in a scene, can also be offloaded, so long as the software properly divides up the tasks Source

Other quotes:

the Xbox One is an engineering marvel that combines both cloud processing and a heavily engineered game console to produce game effects that Microsoft promises will be truly impressive. Source

For the last 40+ years we have incrementally improved graphics through better local hardware. We have been adding cores, increasing clock speed, upping RAM etc. We can easily understand this upgrade. The Xbox one's cloud capabilities are difficult to explain and, as you could imagine, had Microsoft spent any time at E3 explaining the above things the damage would have been even worse. Orleans, free Azure resources and deep integration into the Xbox one will assuredly create new experiences. I am positive, after we experience and witness the benefits of the cloud, we will spend less time worrying about a few cores. This cloud will become stronger and more efficiently used. Microsoft dumps over $9 billion worth of money just to research cloud capabilities. If you read their whitepapers, they put a heavy emphasis on cloud technologies that are going to benefit the Xbox one. It's truly an exciting time we live in, where we get to say billions of dollars are being spent every year by one company to improve their console. Microsoft spends more R&D, just on the cloud, than their competitors (console and PC) spend on their entire R&D projects across all offerings(I don't have more recent figures than this). We could be angry about DRM, digital, the removal, etc. That's OK - just don't fall into the trap of "Microsoft doesn't care about us" and that any money you give them hurts gamers. Microsoft spends 17% of their profits on research and development, more than any of their direct competitors in any marketspace. Know the extra $100 is not simply for the Kinect. When Microsoft says they are over-delivering value for the price, this is why.

It's worth noting, and I'll post another time, that Microsoft pulled over their top visionaries and engineers to solely focus on Xbox development. This includes pioneers of the cloud industry and they even dedicated the chief architect or "father" of Windows NT/2000/2003 to Xbox. This guy was given the distinction of "Technical Fellow" which only 22 employees in all of Microsoft's history have achieved. They gave him to us. They then moved over the Azure hypervisor director to the Xbox group. Gamers are being taken seriously both for the PS4 and Xbox one. It's a marvelous time to be a gamer.
Source

EDIT: toned down the excitement of the last two paragraphs to keep it from detracting from the rest of the post.
EDIT 2: Added source for the job swaps
EDIT 3: I posted this for /r/xboxone who is largely not frothing at the mouth to argue PS4 vs Xbox one. This allowed me to talk candidly about cool technology being produced by Microsoft research labs and how it is effecting the Xbox one. So if this gets cross-posted, please keep that in mind folks. Happy reading!