It's a cross between AR and VR in which a different virtual world is inserted into the real world [1]. It predates the term, but the HoloChess scene in Star Wars is to me a good example. The contrast is with AR, in which the real world is annotated with virtual info, and VR, in which the real world is hidden. But the terms are a bit blurred.
This isn't how Microsoft is using the term. For them it's essentially a hollow marketing differentiator and a way to lump Hololens and inside-out tracking under the same banner.
To all intents and purposes just substitute "VR" whenever Microsoft says "Mixed reality".
Since when does augmented reality only annotate the world? This seems to be a meme spread by Google Glass, which wasn't even augmented reality since it didn't use reality in any way.
[1] https://en.wikipedia.org/wiki/Mixed_reality