"Nanowood" as the team calls it, is produced by taking certain cuts of regular wood –American basswood in initial trials – and chemically removing all the lignin from it. Lignin contributes the yellow/brown color and hardness you'd normally associate with wood. It's removed entirely when making perfectly white paper that doesn't yellow as it ages.
In fact, the process for producing nanowood is very similar to making paper – the wood is cut, paying special attention to its grain, and then it's boiled in sodium hydroxide and sodium sulfite, then treated in hydrogen peroxide to remove lignin and most of the hemicellulose, and then freeze-dried to maintain the structure of the wood, instead of mashed up as you would to produce paper.
With the lignin taken out of a block of wood, what you're left with is a lightweight, white bundle of cellulose fibers – the scaffold-like structure of the wood itself.
These fibers not only act as extremely effective insulators that are significantly better at blocking heat than the styrene- or silica-based materials typically used in home insulation, but their tubular shape also gives them anisotropic properties. Heat can conduct fairly freely in line with the fibers, but is very effectively blocked in any other direction. So designers can use this property to channel heat around the place as they see fit, and block it elsewhere, just by changing the orientation of the nanowood fibers.