When an LCD pixel darkens, it polarizes at 90 degrees to the sandwiching polarizing screens. This cross-polarizing blocks light from passing through the LCD screen where that pixel has darkened. The pixel darkens in proportion to the voltage applied to it: For a bright detail, a low voltage is applied to the pixel; for a dark shadow area, a higher voltage is applied. LCDs aren't completely opaque to light, however; some light will always penetrate even the blackest LCD pixels.
Moving pictures on a CRT TV do not exhibit any sort of "ghosting" because the CRT's phosphor, charged by the strike of electrons, emits most of the light in a very short time, under 1 ms, compared with the refresh period of e.g. 20 ms (for 50 fps video). In LCDs, each pixel emits light of set intensity for a full period of 20 ms (in this example), plus the time it takes for it to switch to the next state, typically 12 to 25 ms. The second time (called the "response time") can be shortened by the panel design (for black-to-white transitions), and by using the technique called overdriving (for black-to-gray and gray-to-gray transitions); however this only can go down to as short as the refresh period.
This is usually enough for watching film-based material, where the refresh period is so long (1/24 s, or 41.(6) ms), and jitter is so strong on moving objects, that film producers actually almost always try to keep object of interest immobile in the film's frame.
Video material, shot at 50 or 60 frames a second, actually tries to capture the motion. When the eye of a viewer tracks a moving object in video, it doesn't jump to its next predicted position on the screen with every refresh cycle, but it moves smoothly; thus the TV must display the moving object in "correct" places for as long as possible, and erase it from outdated places as quickly as possible.
Although ghosting was a problem when LCD TVs were newer, the manufacturers have been able to shorten response time to 4ms on many computer monitors and around an average of 8 ms for TVs.
There are two emerging techniques to solve this problem. First, the backlight of the LCD panel may be fired during a shorter period of time than the refresh period, preferably as short as possible, and preferably when the pixel has already settled to the intended brightness. This technique resurrects the much hated flicker problem of the CRTs, because the eye is able to sense flicker at the typical 50 or 60 Hz refresh rates. Another approach is to double the refresh rate of the LCD panel, and reconstruct the intermediate frames using various motion compensation techniques, extensively tested on high-end "100 Hz" CRT televisions in Europe. The best approach may be a combination of two, possibly allowing the viewer to switch them on or off when viewing video- or film-based material.