Color spaces are a way of representing color as one a tuple of numbers, typically as three or four values. Color spaces lend themselves to (in principle) reproducible representations of color, particularly in digital representations, such as digital printing or digital electronic display.
CMYK is a subtractive color space used in the printing process. One starts with a white canvas, and uses ink to subtract color from white to create an image. CMYK stores ink values for cyan, magenta, yellow and black.
HSV is often used by artists because it is often more natural to think about a color in terms of hue and saturation than in terms of additive or subtractive color components. HSV stores a hue value, a saturation value and an intensity value.
Once you've decided which color space you want to work in, if you are working on a computer, you must then address the problem of color space encoding.