The monitor (and LCDs in general - try a calculator) uses polarisation to display light and dark areas, by manipulating different areas via an electric field. As a result, the light that is produced is polarised as part of the function of the monitor, meaning that the filter will block it out if aligned correctly.
More detail:
An LCD screen is made up of two polarised layers. When switched on and operating with no field across an area (pixel), the polarisation of these layers is aligned and you see a "lit" area coming from the backlight behind. By applying an electric field to one or more areas of one of the two layers, we can orient that layer at 90 degrees polarisation to the second, meaning that no light from the backlight can pass through, creating a "black" area.
By putting your polarisation filter in front, you're manually doing what your monitor does via an electric field application to display a black screen.