PANTONE was founded in 1962 by Lawrence Herbert, now the current CEO, Chairman and President of the company. At first, Pantone was nothing more than a struggling, small business which manufactured color cards for cosmetics companies. Herbert soon acquired Pantone, and developed the first color matching system in 1963.
Primary among these products are the Pantone Guides, which consist of a large number of small (approx. 6×2 inches or 15×5 cm) thin cardboard sheets, printed on one side with a series of related color swatches and then bound into a small flip-book. For instance, a particular "page" might contain a number of yellows varying in luminance from light to dark.
In theory, the idea of the Pantone system is to pick colors from the guides that you like, and then use their number to specify how to print the output. One might ask the print shop to "print this area using pantone 655". The print shop will have instructions on how to produce color 655 on their equipment, and the output will look as you expect.
In reality there are numerous subtle diffences in the abilities of various devices to output a full range of colors. Printed materials use the four-color CMYK system, while on-screen displays on computers use the RGB system, and matching between the two can be notoriously difficult. While the Pantone system works reasonably well amongst various machines of the same ilk, moving from computer screen to printed output - how almost all publishing is done - is seen by some to be still largely hit-and-miss.