The short answer.
The TV screen is divided into numerous picture elements (pixels), which are the basic units of display in a television. The colour and brightness of each of these individual pixels makes up for an image on the TV. An individual pixel is made of 3 sub-pixels - RGB (Red, Green and Blue - the primary colours). The brightness of each of these sub-pixels is varied in order to produce a desired colour. When each of the pixels displays different colors and brightness, the image is produced on the TV.
The LED TV consists of an LCD (Liquid Crystal Display) panel. The panel is made up of numerous LCD cells. Three of these cells (corresponding to RGB sub-pixels) make up one pixel. To get a better understanding of the pixels and sub-pixels in an LED display, have a look at the image below.
Closeup view of a typical LED display.
The above picture is a closeup view of a typical LED display. It should give you a fair idea of the pixels and sub-pixels.
Behind the LCD panel, there is a uniform LED light source. Each LCD cell can be controlled by electric signals to let out a controlled amount of light as per the signal. Thus each individual sub-pixel can be bright or dark or anywhere in between, as per the electric signal. This is then passed through the colour filters - Red, Green or Blue to get the required colour. This then reaches the viewers eye where the image is seen by the viewer.
All of the above happens to produce a single image. A video is produced by rapidly displaying one image (frame) after another, so that there is a sensation of motion and we see the series of images as a video.
The long answer.
An LED TV is made up of multiple display components. On the back of the LED TV, there is an LED light source. In front of this there are light diffusers that uniformly distribute the backlight from LED source to the LCD panel in front. Next is the LCD panel, which produces the images that we see in the TV. Let us get to each of the sections in detail.
LED Light Source
The LED light source is located at the back of the LED TV. This provides the back light for display of the images on the TV. The LED TVs are similar to the LCD TVs that were prevalant some time ago. The difference being the back light source. In case of earlier LCD TVs, the backlight was from CCFL ( Cold Cathode Flourescent Lamp ). In case of LED TVs, it is the LEDs. The LEDs are more energy efficient than the CCFL lighting. Thus the current LED TVs consume lesser energy than the earlier LCD versions.
The LED light source comes in two variations.
Full array LED - In this case the LED light sources are placed uniformly on a back plane. See the image below to get a better picture.
Full Array Backlit LED Example.
Edge lit LED - In this case the LED light source is located on the edges of the panel. See the image below to get a better picture.
Edge Lit LED Example.
In general, the full array LED backlight provides a better picture. This is because, many LED TVs use a technology called Local Dimming. What is done here, is that the backlight in the darker regions is dimmed to provide a better black level. This enhances the contrast ratio of the TV, providing a better picture quality. This can be done much more effectively in a full array LED because, a region can be dimmed more effectively than in a edge lit LED.
The picture production on the LCD panel requires that the light be uniformly distributed in the backplane. This is accomplised by light diffuser sheets. There will be multiple light diffuser sheets placed between the backlight and the LCD panel to provide the LCD panel with source of uniform backlight.
The LCD panel
The LCD panel is made up of multiple Liquid Crystal cells. It is these cells in combination with the other components that generates the image on the TV. Let us go into more detail of how an LCD panel works below.
Consider the image below.
Liquid Crystal Cell.
The light enters from the backlight and it emerges towards the viewer. An LCD cell consists of two polarizers, liquid crystal molecules, electrodes and color filters. The first polarizer is located at the point where the light enters the cell. This polarizer polarizes the light in a single direction. The second polarizer is located at the point where the light exists the cell. This polarizer polarizes the light in a direction that is perpendicular to the first polarizer. The liquid crystal molecules are located at the center of the cell in between the polarizers.
The function of the liquid crystal molecules is to change the direction of polarization of the light. The amount of direction change depends on the alignment of the liquid crystal molecules. When there is no electricity applied, the liquid crystal molecules are not aligned and there is no change in the direction of polarization of incident light. When this light tries to exit the second polarizer ( that polarizes the light perpendicular to the first ), no light can escape, since the polarization is perpendicular to the first polarizer. This results in a dark pixel. Now, if some electricity is applied to the liquid crystal, the molecules of the crystal aligns so as to change the polarization direction proportional to the applied electricity. When more electricity is applied, the liquid crystal twists the the light polarization, which in turn, causes the second polarizer to allow more light to pass through. Thus, as the strength of the electric signal that is applied to the liquid crystal is increases of decreases, the light that is emitted out of the liquid crystal cell increases or decreases.
Depending on the alignment of the electrodes are aligned in the liquid crystal display cell, we have different display variants - Twisted Nematic (TN), In-Plane Switching (IPS) and Vertical Alignment (VA).
Finally, the emitted light is passed through the color filters. Three of these filters - R, G, B (Red, Blue, Green) of one particular liquid crystal cell, through the varied intensities of lights in the Red, Blue and Green, produce a single colour of a particular intensity.
When each of the liquid crystal cells produce the light of required intensity, the picture is displayed on the TV.