Aerogels are an amazing material for a variety of reasons. But one of the big ones in relation to energy modeling and buildings is their amazing properties of insulation. Hell, they are the reference image on the R-value wikipedia page.
So what are aerogels? They are the lightest solid in the world, due to their extremely porous nature, being over 90% air. They were first discovered in the 1931's when two chemists bet who could replace the liquid in a gel material with a gas without causing the original form of the gel to be altered. The resulting material where the liquid component of the gel has been extracted though supercritical drying is 'Aerogel'.
The low thermal conductivity of aerogels have made them a very attractive possibility as a building insulation material. One big factor holding them back, as referenced in the video, is their fragile nature. Fortunately, a new type of polymer aerogel was recently developed at NASA's Glenn Research Center in Ohio. They've basically solved the fragile nature of aerogels by creating a polymer variety that is 100 times strong than typical silica based gels and can be manufactured in thin flexible film form.
If the commercial cost of production can be pushed low enough this would open the door for applications of this material in the building sector and many other industries. If you want to read more about the development check out the NASA research paper on the development, or the more manageable informational brochure.