Although it is theoretically possible to achieve true black by combining cyan, magenta and yellow, it does not work in real world situations. Because inks do not combine in the same way that light does cyan, magenta and yellow when mixed together yield a deep purple-brown that is far from the expected black. Therefore, printers use four inks (CMY and black-K). Using K allows a true black as opposed to the purple/brown that is yielded by the combination of CMY. There are more complex reasons for using black in addition to CMY.
Regular color printers like the ones that can be used with personal computers create the illusion of color by placing several dots of cyan, magenta, yellow and black very close to each other, so close that they seem to bleed together giving the illusion of color. The technique is very similar to the pointalism of the early 20th century. The illustration below (which is borrowed from the May 1992 edition of MacWorld Magazine) shows a desktop CMYK printer applying several dots of its four inks in order to create the illusion of color.
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