Ink-jet printers have been popular for a long time because they are relatively cheap to buy and most of them can combine both black and white and colour printing at the same time.
These printers use cartridges which contain ink. They operate by heating the ink as it flows through the nozzle. The heating process causes a small droplet of ink to form. This is then released as a single dot which forms part of a letter or image. This is why the printouts often come out of an ink-jet printer still slightly wet.
They are also called 'impact printers'. The print head contains a grid of pins and different combinations of pins are pushed out to form different characters. The print head then hits a carbon ribbon leaving an imprint on the paper. This makes them fairly noisy as you can hear the pins striking the paper.
Dot-matrix printers are ideal when you need carbon copies. This is because the print head hits the paper with enough force that when carbonised paper is used, the impact makes a copy on the second sheet.