"The appliance which kept a whole generation up at night while it operated." -- Pseudo_Intellectual
From a technical standpoint, the Dot Matrix Printer is one of the most (physically) complex devices common in the computer world, and has had a life as long as any other technology with the possible exception of the Keyboard.
A Dot Matrix printer uses a matrix or grid of pins (also called 'wires') assembled in parallel and each connected to a magnetic actuator. Common amounts of pins were 9, 12, 18 and 24 pins. When an actuator is fired the tip of the pin moves out of the assembly it it housed in (called the print head) and strikes a sheet of paper. However, in between the sheet of paper and then pin is an ink impregnated strip of cloth, usually polyester, called the 'ribbon'. The upshot of this is a very small dot of the fabric of the ribbon is slammed into the paper transferring a very small dot of ink on to it. The actuator is then relaxed and the pin moves back in to the print head.
The print head has a whole is moved along the width of the paper (also called the carriage of the printer) on a motor driven assembly controlled by circuitry that is aware of it's position in relation to the edges of the paper. When the printer receives data, it moves the print head in a controlled fashion along tightly-spaced parallel lines on the paper and as it moves it triggers the print head pins in various patterns to transfer ink to the paper as the print head moves.
After the print head has been moved from one end to the the other end of the carriage, a motor attached to the platen advances the distance necessary in order for the print head motor to move the print head in a way that the next line of ink will be coherent with the previous lines.
Dot Matrix printers are very significant in the computer world because they were the first printers that allowed for a changeable typeface without replacing the print head itself as you would have to do with a Daisy Wheel Printer. They are also important because they were only the second device that could print free-form graphic images, the other device being the plotter. Plotters were then, and still are now, horridly expensive.
A notable feature of some dot matrix printers, first seen in expensive models and then in economy models later on, is a feature called "Logic Seeking". Under normal circumstances the head starts at one end of the carraige and then runs the print head across the page printing until it reached the other end, and it then returns it to the starting edge of the carriage without the print head firing. A Logic Seeking printer is a printer that fires the print head in both the advancing and returning strokes of the print head assumably doubling print speed (though in real terms it probably only increases it by %30 or so). An example is the Apple Imagewritter which was logic seeking in text mode, but not in graphics mode.
Even in the 21st century, dot matrix printers are still the workhorse of the business world. There is no Laser, Inkjet or other printer that can come close the the printing speed and cost per page as a hefty old dot matrix printer. Sure, they're no where near laser-quality, but when I'm printing out reams of only source code do I care? Most people would rather get NLQ at 5 PPM at $.002 per page using their Epson FX80 than get 900x600 resolution and 2 PPM at $.02 per page in a fancy laser printer.
Just don't expect people to take your resume' seriously if printed on a 9-pin Epson.
My old Printer story: At an old gig I used to slave at in PC repair there was an old printer hooked up the the Mini they used for EDP. I want to say it was an IBM 4850 but I'm not sure of the model number. It was huge and affectionately known as "the shake and bake" because it could shoot out nearly 20 Pages Per Minute and walk across the floor while doing it. One day as I was doing something in the machine room, an IBM service tech came by to do some PM on our AS/400. He looked at the printer, then at me sitting on top of it. "Did you know," he began, "that printer is probably twice your age?" I didn't believe it was that old, but then he pulled open a service panel and showed me the manufacturing inspection sticker -- September 3, 1976. This was in 1999 and i was 20 at the time. Not twice my age but close. To my knowledge they're still using it.