The way they make the display feel like glass is because it (kind of) is. Originally folding phones used polyamide (a type of plastic) for the cover layer of the screens, and these had a plasticity feel to them, but some newer foldables use UTG (ulta thin glass) basically a glass-like material that is so thin that you are able to fold it.
The other part of the screen below the layer you interact with are made with materials that are also flexible.
You can find a more detailed answer here https://www.androidauthority.com/how-do-folding-screens-actually-work-3164822/
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