Holographic storage works on the same principle as holograms do: you take a laser, split it into two beams (the data beam and the reference beam), bounce the data beam off of an object, and then recombine it with the reference beam onto a photographic plate.* Instead of storing an image of the object, the plate stores the interference pattern produced with the two beams combine with each other at the plate. This pattern contains much more information about the object than a picture does: it's actually a representation of the entire light field reflected by the object, allowing you to see the object from multiple angles and in three dimensions.
In terms of storing data holographically, the principle is generally the same, except that instead of bouncing the data beam off of an object, you bounce it off of an array of tiny electromechanical mirrors that either reflect the light or don't, creating a holographic "page" made of up of an array of bright spots and dark spots, which is how your data are stored. Once a page is "written," you can slightly alter the angle at which your laser intersects your storage medium, and then record another page. To retrieve the pages, you just shine a laser into your storage medium at the exact same angle that it was stored at, and the holographic "page" pops right out.
If you've got a three-dimensional storage medium like a holographic cube (which in this case is a lithium niobate crystal), the amount of data that you can store is limited only by the volume of the material itself and the precision with which you can control the read/write angle, meaning that you can store a lot of data in a very small space. AON says that their current capacity roadmap tops out at just under 10 terabytes, with a data transfer rate of 1.2 terabytes per second. Furthermore, holographic data are stored permanently (there's no degradation), they system as a whole is extremely robust, and the price per gig is well under $1.
Generally, we're not fans of the "we have this super-secret awesome technology but you can't see it or know how it works" type of pitch, but enough similar technology exists that we're willing to believe that AON's just about ready to bring volumetric holographic storage to market, provided that they can find the right partners to throw some funding their way.
*It's actually very simple, and a lot of fun, to make holograms at home. You can buy a kit with everything you need to do it and 20 plates for under $100. LINK