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The fabric is called Deflexion, and it's made by Dow Corning, the same guys who probably made the silicon that's running your computer right now. The Deflexion material is also made from silicon, except it's been polymerized into flexible silicone sheets with a special molecular structure.
Most of the time, the molecules in the silicone move around each other freely, but if something hits them, the molecules bunch up and instantly turn solid. This absorbs and disperses the impact, just like a solid piece of armor would.