An LCD display is composed of a technology based on the properties of liquid crystals and, more importantly, depends on the way the liquid crystals are embedded on the matrix.
The following is a schematic of a LCD cell I got from HowStuffWorks
LCD's work by changing the angle at which light passes through them:
If we apply an electric charge to liquid crystal molecules, they untwist. When they straighten out, they change the angle of the light passing through them so that it no longer matches the angle of the top polarizing filter. Consequently, no light can pass through that area of the LCD, which makes that area darker than the surrounding areas.
If the LCD matrix is disrupted, light may not pass as it should. Light may be completely blocked, or may be completely passed. This creates an effect know collectively as a dead pixel (although, as Wikipedia points out, there is a technical difference between dead and stuck).
This happens if you place too much pressure at one point of the display, or by natural causes (due to heat, temperature, humidity, or sagging occurring at the surface level). It also explains the rainbow-colored effect that happens while you press the display: the crystals are being moved (microscopically) from their original positions and light passes at a new angle, that then diffracts.
Comprehensively it is hard to take a screenshot of the problem (as the display signal is working right). I managed to get this image from Google, the dead/stuck pixels are the light dots on the display.
To fix this, a good way is to simply (and gently) tap the area surrounding the dead pixels with a blunt object (a stylus or a pen cap). That will force the crystals inside to rearrange to their original positions.
However, crystal display are quite resilient, as @50-3 stated. Mainly because the display is somewhat rigid due to the amount of circuitry and connecting films.
As you can see in the diagram, there exists a light source behind the LCD film. That usually was a set of florescent bulbs (in older models) and in some badly-made models some light could be seen from the seams that hold the film to the display.
More recent developments in LED technology have made it possible to use that as back-lighting.
LED (Light Emitting Diode) are simply a set of two doped silicon pieces that, when electricity runs through them, create an effect similar to a voltaic arch. Quoting from HowStuffWorks:
They are illuminated solely by the movement of electrons in a semiconductor material, and they last just as long as a standard transistor. The lifespan of an LED surpasses the short life of an incandescent bulb by thousands of hours. Tiny LEDs are already replacing the tubes that light up LCD HDTVs to make dramatically thinner televisions.
This is a LED (retrieving the schematic from Wikipedia):
I assume any one has at least seen one, because the are everywhere. Now, think that it can be reduced to about a fraction of their size, placed millions of them on a board, and give them colors.
There you have an LED display. LED displays have two main differences in regards to LCD:
1. They are more durable (i.e. no moving (or flowing) parts).
2. They don't require back-lighting (LED's provide heir own light).
This being said, since LED's are just a piece of silicon, they are as durable as the silicon board that holds them all together. And they can take as much abuse as any board can take. So, they are impervious to nudging and impacts, to some extent.