RGB is an additive color model. Colors are created by adding variations of red, green and blue. The combination of all three creates white. RGB is additive because the addition of the red, green, and blue wavelengths creates color. The combination of all three creates white light.
CMYK is a subtractive color model. Colors are created by combining cyan, magenta and yellow. The combination of all three creates black. CMYK is subtractive because the combination of cyan, magenta, and yellow takes light away and is covering up the white light. The wavelengths of those colors combined creates black, which is the absence of color.
The problem when designing is that not all RGB colors translate to CMYK colors. RGB is used in digital forms – cameras, televisions, computers, and phones. CMYK is used by printers for printing. Both models have a large, but finite range of colors that can be created. The RGB spectrum is larger though, so there are RGB colors that can be created that are not even in the CMYK color spectrum. The process by which the different colors are created is what leads to these differences.
So ultimately when you are designing you have to first establish what medium. If it will be displayed on a screen then use RGB. If it will be printed then use CMYK. Since there are more RGB colors than CMYK, it is beneficial to always design in CMYK, so that your colors have a better chance of translating. If you do use a RGB color that can’t be translated to CMYK then you will have to settle for a color that is close if you ever need to print. It is also important to note that using CMYK assumes that the paper will be white. Most common printers don’t have white ink, so if your paper is not white, any white on the screen will actually turn out to be the color of the paper.