It’s important to remember that in the entire visible color spectrum we can only reproduce a limited amount. Whether it is on screen with pixels or in print with inks/toner there are only a certain range of colors that can reliably be shown or printed.
RGB (or what you see on your TV, monitor, or mobile device screen) has a pretty wide gamut (color space) but it is still far short of every color you can possibly see. As technology improves, RGBs gamut is increasing (e.g. Colormatch RGB, Adobe RGB 1998, and ProPhoto RGB). However, what you see on a computer screen may be irreproducible on press. Be sure when working on projects for print to use a color profile in applications like InDesign or Photoshop (e.g. U.S. Web Coated (SWOP) v2, U.S. Sheetfed Uncoated v2, and US Newsprint (SNAP 2007)) to ensure what you see on screen is limited to what can be printed on paper or other printed substrates.
RGB is written using 0–255 for Red, Blue, Green pixels shown on the screen. (e.g. black=R0 G0 B0, white=R255 G255 B255, Green=R0 G255 B0, Yellow=R255 G255 B255), and so on).
CMYK is a limited color set and used by printing presses, toner copiers, or your home ink jet. Very small dots of Cyan, Magenta, Yellow, and Key (Black) inks are combined to form many different colors. Impurities in these inks prevent achieving as many colors as you might like on a printed surface. The color gamut can vary widely based on what substrate you are printing on (e.g. Coated paper, Uncoated paper, Tee Shirts, Newsprint, Vinyl, etc.). Some of these limitations have been ameliorated by press techniques such as using hexachrome, PANTONE inks, or if you have a high end ink jet printer you may notice it has 6, 8 or even 12 colors in order to achieve an even wider color gamut. Even these can only approach a portion of what is possible to reproduce in the RGB space.
CMKY is written using 0–100% for amounts of Cyan, Magenta, Yellow, and Key (Black) inks or toner combined to form a color. (e.g. white=C0 M0 Y0 K0, Green=C100 M0 Y100 K0, Yellow=C0 M0 Y100 K0, and so on). In CMYK printing black can be just 100% of black ink or a darker form of rich black (e.g. rich black=C50 M40 Y35 K100.) Don’t ever use C100 M100 Y100 K100 as presses can only accommodate a certain percentage of ink coverage. This is usually no more than a total ink coverage of 260-320%, depending on your press and the paper being printed on. (e.g. C50 M40 Y35 K100 would = 225% total ink coverage.) Before printing check with your press to see what their press specs are for color. They may even have custom color profiles which can be used in Adobe creative applications.
SPOT colors. These are the individual pigments (similar to acrylic paints) that are used on an offset press or silkscreen to achieve a pure single (or two or three or more) color(s). The PANTONE system of inks are one way of creating SPOT colors (see below). There are other systems as well (e.g. TOYO, RAL, etc). Often when making stationery (letterhead, business cards, etc) SPOT colors will be used to achieve a clean pure color. These SPOT colors span their own color gamut, wider than CMYK’s. Colors include fluorescent and metallic inks.
PANTONE is a proprietary SPOT color system that allows people to share a standard set of color choices. If most of your work is going to be printed on a web offset or gravure press (e.g. most magazine and newspaper advertising), since they mostly use the CMYK gamut there is a danger of selecting a PANTONE Coated (C) or Uncoated (U) color that is not possible to accurately reproduce without using specific a SPOT color ink (CMYK is approximately half of this color space.) The PANTONE Color Bridge is useful in selecting colors, which can nicely convert into RGB or CMYK analogues and crosses over well from C to U paper stocks.