This new holographic display from Microsoft, called Vermeer, is certainly not the first "touchable" hologram that we've seen. But every other system places the holograms themselves behind glass, while with Vermeer, it's hanging out right there in the open, Princess Leia style.
Vermeer is based on a well-known optical illusion toy called a mirascope that can be used to turn small objects into "holograms" that appear to float in space. A mirascope consists of two parabolic mirrors that are sandwiched together with a hole cut in the top one, and anything you hide inside them will magically appear to be hovering above the hole, thanks to the way light is reflected around inside the bowls. You can see a video of this in action here.
Mirascopes usually just work with small stationary objects, but there's no reason that they can't transmit moving images. Microsoft Research has managed to stuff a light field projector and diffuser into a mirascope that can render nearly 3,000 images per second, enabling the display of 192 different viewpoints of a projection at 15 FPS for a seamless, full-motion 3D view. Beyond the mirascope itself, there's no trickery going on here: the hologram doesn't appear in a projection tank and you don't need to wear glasses. It's right out in the open for you to mess with.
Oh, did we mention that you can mess with it? 'Cause you can. Since there's no glass or spinning parts or anything mechanical surrounding the hologram itself, you can poke and prod it as much as you like. And when you do, the hologram can react. One of the crazier things about mirascopes is that since they're just mirrors, they work both ways: putting a real object inside projects a virtual object outside, and at the same time, putting a real object outside will cause a virtual projection of that object to pop up inside the mirascope itself. Microsoft has taken advantage of this, and by putting an IR illuminator and tracking camera inside the mirascope, they can track the virtual image of your hand as it interacts with the virtual image of an object. It's totally trippy.
You can see how it all works in the video below.