RGB stands for Red, Green, and Blue and should be used when you are creating an image for the web that will remain on a digital screen and/or monitor. As such, RGB is a color space for digital images so you should use the RGB color mode if your design is going to be displayed on any screen. The light source in any electronic provides any color you may need by mixing the red, green, and blue together, merely changing its intensity depending on the desired color. The act of the red, green, and blue mixing to create a color on the device’s screen is known as additive mixing, which is when all colors begin as (dark) black while red, green, and blue light is added atop the black in order of how much intensity is needed to make a certain color or pigmentation. In RGB, you may also create a pure white color if you mix red, green, and blue all at the same intensity. RGB comes in handy for designers because they are able to easily change things such as shading, vibrancy, and saturation of an image just by making adjustments to the intensities of any of these three main colors.
CMYK stands for Cyan, Magenta, Yellow, and Key/Black and should be used for designs and works that are to be printed. Even if you begin creating a design in the RGB color mode and soon find that you must print said design, you may simply switch over to CMYK before printing by going to Image>Mode>CMYK Color (specifically Photoshop instructions). CMYK deals with combining these colors in order to print the image; it does what is known as subtractive mixing, which is when all colors begin as a blank white with each new layer of ink reducing the color’s original brightness to create the desired color. Opposite of the RGB color mode, when all colors are combined in CMYK, they create pure black.
In short: You, as a designer, must know the end result of work; if the end result is going to be posted up on the web or seen on any screen, you must use the RGB color mode, while if the end result is going to be printed, you must use the CMYK color mode. Additionally, setting the color mode is as simple as selecting it when you create a new document or later on switching it over to either RGB or CMYK.
The link to where I found my information can be located here.