Basically, imagine Nintendo has a bunch of powerful computer processors set up in a server room at their buildings across the world.
You pay a rental fee to use that processing power they have to play games with enhanced graphical fidelity, or even run more demanding games outright. It's offered to you through cloud technology. You're basically connected to the processor over the internet.
This way, they could realistically sell the console at a much lower price than average, but would make back a lot of money through the cloud processing rental service. For example, imagine the next Zelda game, on the vanilla NX, is basically the same as the Wii U version - hypothetically, I would say upscaled to 1080p resolution, 30FPS, no anti-aliasing or ambient occlusion, or anything like that.
Now imagine you could pay a monthly fee that you can opt out of, let's say...$30 for argument's sake. Pay that fee, and suddenly you can run a lot of your games with some kind of graphical upgrade, like native 1080p, 60FPS, you have some anti-aliasing, and you have ambient occlusion.
This way, the console would be cheap and the processing power is meh, and you simply rent more processing for those bigger games or when you know you'll be playing a lot of games on your NX and want them to look really nice.
Cloud Processing is already a thing so it's not just something I'm making up. There are companies that offer it to other companies and such, so they can run better software and the like, or some companies just use it internally so they don't have to outfit all of their PCs with really powerful tech individually. But it's not really broken into gaming yet, and since Nintendo has patented something that sounds similar to it, I would imagine they plan to be the first to implement it heavily into gaming.