An excellent question!
The same technology that is behind computer screens is also behind other displays, such as your TV or phone. There have been several major technologies for displays. They are the cathode ray tube (CRT) , plasma display , and liquid crystal display (LCD).

We'll start with the common construction of all displays. All displays consist of many small cells known as pixels. If you look really close at an old screen, you'll see the pixels clumped in red, green, and blue. These are the three colors used to generate all other colors. When you put lots of pixels together, you can generate an image that can be viewed at a distance. To create that image/color, you control when each pixel lights up and by how much.

The Cathode Ray Tube Display
If you've ever wondered why old televisions and computers had such a large back end, it was in order to accommodate the CRT technology. A CRT consists of a vacuum tube with electrodes (often a metal) attached to a high voltage source. The high voltage source generates a stream of electrons that are accelerated and deflected with a magnet to hit a particular spot on the fluorescent screen. You can watch a short animated video about the cathode ray tube. In fact, if you were to take a strong enough magnet to an old TV screen, you could distort the image on the screen (and potentially damage the screen)- you're essentially doing the same kind of deflection as the TV!

In order to actually make a screen with color, you need several electron beams that control each color; a mask with tiny holes in it is used to filter out any electrons that hit the wrong color pixel.

The Plasma display
A plasma display is also composed of pixels. Instead of electrons coming from a beam and striking the screen, you excite part of the gas mixture in each pixel to emit a UV (ultraviolet) photon (i.e., radiation, but you can't see it), which in turn excites the phosphor pixel and causes to emit light in the visible (where our eyes can see). In order to get these photons, you need to apply a high voltage and excite the gas (this is essentially what plasma is ). Because you don't have a vacuum tube sticking behind the screen, you can get flat screen TVs.

The Liquid Crystal Display The current technology used for many of the screens we have today are LCDs. With LCDs, we move to a different kind of material known as liquid crystals. What is a liquid crystal? It's a material with liquid properties (e.g., it flows, it takes the shape of its container) but if you zoom in, there's a degree of crystal order! This is pretty surprising since we generally associate crystals with solids. A liquid crystal is composed of a bulky molecule where the structure imposes some degree long-range order (i.e., crystallinity). You can see some pretty images of liquid crystals and example molecules that are liquid crystals here.

The basic set up of a LCD pixel is here. You basically have the liquid crystal between two polarizers that are perpendicular to each other. Light in general can take on a number of directions (i.e., polarizations). Polarizers are layers that only allow a certain direction of light to pass through; if two polarizers are placed perpendicular to each other, no light passes through.

However, putting in a layer of liquid crystals allows you to modulate whether light passes through. It's possible to orient the liquid crystal in a spiral from one polarizer to the other (with electrodes in the middle). The twisted configuration of the liquid crystal twists the orientation of light so light can pass through the polarizers. When a voltage is applied, you force the liquid crystals to align with each other, and light can no longer pass through. (The mirror is for reflecting back external light. This would be how your calculator works. But there are, naturally, LCDs where the back is illuminated as well.) For a color LCD screen, the same principles hold.

An interesting history tidbit. A common problem with CRT-displays was that if the screen was left on a single image for too long, that image would burn into the screen.

Answer #1 continues here:
This is what motivated the development of screensavers. Nowadays, screensavers are made obsolete by LCDs, but they are still pretty fun. You can find a set of pretty nifty screensavers here for free for Linux- and Unix-based systems. I have the same set of screensavers on my computer (my favorite is the bouncing cows).

Another interesting tidbit. If you own an Apple product, you might have heard of the retina display, in which the screen doesn't look like it has any pixels! In actuality, there are still pixels but they are just very small- so small that your eye cannot resolve them individually at normal viewing distance. (But if you look really close, you can still kind of see them.) You can read more about the retina display here.

But the engineering continues! Many people are also working on displays based on organic light emitting diodes (LEDs). These are an attractive alternative as they are much cheaper to manufacture and open the possibility of flexible (and maybe wearable) electronics.

Great question! Images on computer screens (or televisions, iPads, etc.) are made from tiny dots of color, like a printed picture. A dot of color is called a “pixel” and the number of pixels in a certain size screen is the “resolution”. The smaller the pixels, the better the image. See if you can find the smallest dot on a printed newspaper – the low resolution of newspaper makes their pixels easier to see.

Your computer programs need to know the screen size and number pixels to make images. To show a colored image, each pixel is made of three colors – red, green and cyan – which it can mix to make all the colors you see on screen. For a black pixel, it keeps all the colors off. For white, it turns them all on. For pink, it turns red on full but green and cyan on a half strength, etc. You may have noticed that a monitor, projector or TV takes a few seconds to show an image after you plug in a computer – the computer is checking the screen and pixel size, and how fast the pixels can change color.

There are two main types of screens:
1) Light emitting diode (LED) screens are a new technology that uses very tiny lights that are controlled directly by the computer. Since the pixels are small, you can get very detailed pictures with lots of colors. These screens can be thin, flat and use less power for their size. This is what you find in most TVs, laptops and phone/pad screens.
2) Cathode ray tube (CRT) screens were used to make televisions since 1934. They also have colored pixels, but they light up in a different way from LEDs. In CRTs, a glass panel is painted with tiny patches of grey paint that glow in different colors (red, green and cyan). An electron “gun”, controlled by a magnet, shoots electrons at the pixels to make them glow. As you can imagine, the screen needs to be large and far away for the gun to hit each pixel well, so these types of screens are very thick, often thicker than the screen is wide.

What type of screen are you using to view this website? How many CRTs can you find in your house or school?