I think the edge just means CDN edge locations. There’s been a trend towards making edge locations smarter (via Lambda etc), so you can sometimes send dynamic responses straight back from the edge, ie quicker than always deferring to the big data centre for dynamic stuff. Previously computing on the edge was restricted to fairly simple caching of static responses.
In some fields, 'edge' has long been used to refer to devices running in the real world - such as IP cameras and IoT devices that gather sensor data.
I used to work for a company that worked with security cameras, and they always used terms like 'edge analytics' to refer to software that's running on each individual camera as opposed to running somewhere central, like on the DVR the cameras are connected to or a server.
From what I've seen in Nadella's presentations at various events and conferences recently, he's using 'edge' in the same way. Lots of MS presentations about the intelligent edge have included things like training a neural network on Azure, and then pushing it out to IoT devices and phones so the NN is running on 'edge' devices and just transmitting results back to a central server.
Another way to think of it: if we were looking at a tree, servers/the cloud would be the trunk, the internet would be the branches, and edge devices like cameras, various IoT devices, and phones would be the leaves. They're out at the edge of the tree, interacting with the world.
It's the current hot buzzword. It's CDN++, where not just static content gets distributed but web applications get sharded/distributed around the globe to the nearest node to the end user.
I still have no idea what "intelligent edge" is supposed to mean.