The camera on your iPhone or Android smartphone is pretty good. Good enough, and definitely convenient enough, to make most point-and-shoots obsolete. But those cameras will for the forseeable future be limited by their convenience--the need to fit the sensor and lens into a smartphone body (and god forbid, not bulge out from the back) constrains the type of camera hardware that can be used on a smartphone. That's why I think the smartphone is a great complement--not replacement--for a DSLR or large-sensor compact camera. You can buy lens attachments for a smartphone, but not swap out its sensor for a larger or more capable one. Yet.
The DxO One camera is a neat piece of technology that wants to give you the convenience of smartphone photography with the quality of a higher-end camera. It does this by cramming a big 1-inch type sensor and accompanying aspherical lens system into a really compact formfactor--something that weights just 108 grams and is about the size of a GoPro. And it can do that by not incorporating any sort of viewfinder or LCD display. That idea isn't new--Sony has its QX "lens-style" cameras that use a smartphone as the brains and viewfinder, but those cameras transmitted a video signal over Wi-Fi. The DxO One, which only works with iOS devices, sends its data back and forth over an Apple Lightning connection. Low latency, high bandwidth, resulting in a much more seamless and responsive camera experience.