The video you show is of a liquid crystal display (LCD) monitor, also known as 'TFT'. The 'trick' depends on the specific design characteristics of these monitors (described below) and will not generally work with other types of displays such as LED and PLASMA displays.
All liquid crystal displays (LCD) operate on the principle of being able to 'twist' polarized light as it passes through a 'nematic' liquid crystal. The orientation of each liquid crystal in a display is governed by an electric field applied to a transparent electrode, through an array of thin-film transistors (TFT). The liquid crystal is normally 'sandwiched' between two polarizing filters at 90 degrees to each other. Polarized light enters the back of the liquid crystal from the back-lit LED. When the nematic crystal is not energised, it 'twists' the polarized light by 90 degrees so that it passes through the second polarizing filter. Wnen an electric field is applied to the liquid crystal, the light does not get twisted so gets blocked by the second polarizing filter.
See this video for an animation of the nematic liquid crystal: https://www.youtube.com/watch?v=Bf3547WB5qs
For more detail on the internal workings, including a'tear down' of an LCD-TFT monitor see this video: http://www.engineerguy.com/videos/video-lcd.htm
By taking out the second polarizing filter and placing them on a pair of glasses, the display appears 'invisible' (white) to the naked eye because ALL the from the LED backlight that passes through the first polarizing filter gets through the TFT section to the naked eye, regardless of it's orientation (polarization) so the naked eye sees it as 'white'. It's not until the second polarizing filter is applied to 'filter' the light from specific pixels which have 'twisted' their light (with respect to the other pixels) that we can distinguish between the pixels.
Note that the 'trick' is not really very secure if intended to prevent 'evesdropping', sinces anyone with polarizing glasses (including polaroid sunglasses) will be able to read the display.