The Pantone Matching System
The first color matching system for designers was developed by Pantone in 1963. The primary tool in the Pantone Matching System was the Pantone forumula guide. This guide was designed to allow graphic designers and printers to communicate color by referencing a Pantone number. This was a huge improvement, as in the past every ink company had their own color system and there was no way to correlate "Firecracker Red" from one ink company to another. The Pantone formula guide was also built around an ink mixing system, which made it much easier for ink companies to provide consistant color accross multiple locations. Early versions of the Pantone formula guide had 747 different colors, on coated and uncoated stocks.
This concept, of color consistency from designer-to printer-to ink maker-to client, is the real strength of the Pantone Matching System. If everyone in the process has a Pantone formula guide, they can look at the same 185 red, and they are all seeing the same color. The designer specifies a color, the printer orders ink in that color, prints using that color, and the client gets exactly what they want. This end to end color control explains why Pantone has become the worldwide standard for color since it's introduction.
Today's Pantone Matching System features 1,114 Pantone solid colors, printed on coated, uncoated, and matte papers. Each page contains 7 colors, with ink mixing formulas. View a page from the coated formula guide. The pages also include an RGB icon 
, indicating colors achievable on-screen, and an CMYK icon 
, indicating colors achievable in CMYK color printing. Colors that bear both the RGB and CMYK icons are ideal choices for designs that will be reproduced using multiple processes.
Software developers have also made it easy for designers to incorporate Pantone solid colors in their design projects. There are some issues, however. The Pantone formula guides are printed using inks and pigments, while computer monitors reproduce the colors using Red Green and Blue light. This issue causes a lot of confusion due to the different appearance of printed Pantone colors and viewed Pantone colors (on a computer monitor). That's why it advisable to only use a Pantone formula guide to specifiy or determine a Pantone solid color.
More information on Pantone solid formula guides here.