The panel surface is made of glass. A manufacturer known for LCD-TFT displays is Corning. As far as we know, they have 2 kinds of glass: 1731 with a thickness of 0.7 mm and Eagle 2000 which is only 0.5 mm thick.
A panel is basically a sandwich type of construction with a liquid between two glass plates. Both of the glass plates are kept at distance using "spacers". Once the panel is press on with a finger, the local electrical properties change because the distance is altered by some micrometers, among other things.
To those who seek to further dive into this topic, we recommend the advice to pay a visit to the highly informative website of corning.
Another thing worth to pointing out in this context would be the press release by Philips showing a so-called "mother glass" of the 5th generation.
Another coating, which is said to polarize, widen the viewing angle, increase the contrast and reduce reflections, is superimposed from the outside. One of the manufacturers producing such foils is Sumimoto Chemical. Such a protective coating is, again, made of several layers that promise to make the properties mentioned above happen.