It looks like a big, smashed, dirty piece of gum, and feels like a sneaker.
What you are looking at is condensed, raw Gore-tex.
This stuff is pulled using a huge, strong machine into a thin, semi-translucent layer. You can actually pull and stretch it out by hand, but not to the point where it needs to be.
The thinned out Gore-tex membrane is layered between fabrics and protective layers, and is stretched thin enough to create billions of pores that are 1/20,000 the size of a water droplet. This allows the fabric to breathe, but are small enough to not allow water droplets to penetrate.