The same colour is produced differently on a screen and on paper, so the colours of a brand identity have to be specified in several systems. RGB is the system of screens, named after the initials of its primary colours (red, green, blue), and every colour comes from mixing their light. On the web we use its hexadecimal form, for example #FFDC00.
CMYK is the system of printers, in which four inks, cyan, magenta, yellow and black, mix on the paper. Because ink absorbs light, fewer colours can be produced in CMYK than on a screen, so very vivid, neon shades come out duller in print.
Pantone is a standard colour catalogue in which every colour has its own number. The printer prints these colours with premixed ink, so a company colour looks the same on a business card and on a shop sign, wherever they are made. It costs more than four-colour printing, so it is worth using where the colour is the most important mark of the brand.
The paper affects how colours come out as well. The same CMYK colour is more vivid on glossy, coated paper and duller on uncoated or recycled paper, so for important pieces we check with a print proof that the result gives the expected colour.
Screens differ too, because every monitor and phone displays colours slightly differently. That is why we compare brand colours with the printed swatch of the Pantone catalogue and with the print proof, and no single display can be the benchmark.
What this means for your brand
When designing a brand identity we define every colour in each system, and check that they give matching results in print and on screen. A colour that only looks good in RGB will be a disappointment on printed materials. The codes go into the brand guidelines, so the printer and the web developer work with the same values. If an existing identity only has screen codes, the print versions can be defined afterwards as well, checked with a print proof.
You need to pay attention to this in a finished print file too. Images made for screens and saved in RGB can shift in colour when printed, so during prepress we convert every piece to the right colour profile.