CMYK is the colour model associated with litho (offset) and digital printing. Other interchangeable terms to describe it is four-colour process printing or simply full colour printing. CMYK is able to produce the entire spectrum of visible colors through the process of half-toning. When designing for Print the CMYK process is used, and here the key (K) is the black ink used alongside Cyan (C), Magenta (M) and Yellow (Y). It is important to remember this in your design as just using the black ink will not always give you the truest black.
CMYK black (100K) is great for text, allowing for a crisp and sharp reproduction. In fact, at repro stage, your printer in all likelihood will convert any black text to 100% process black, eliminating any registration issues and ensuring best results. However on larger black solids, 100K on its own doesn't really have much impact as black, it prints more as a dark grey/brown. This is particularly evident on uncoated paper stock. And we thus incorporate the other process colours to get the right black print.
The 3 primary colours (CMY), combined on their own, won't produce a fully saturated black and process black is added as the key ink to bring out the best result on solids. This has become known amongst the design and print trade as Rich Black. There are a number of variations, and designers talk about a Rich Warm Black or a Rich Cool Black. Also the best CMYK combination will also depend on the print press on which the job is being run and you should consult your printer for advice. At the end of the day a common formula for print houses is C=60 M=40 Y=40 K=100 (240% ink Coverage) or C=40 M=30 Y=30 K=100 (a bit less than average), and it is around these you will most likely work from.
And if printing black turns out not to be so straight forward, we also need to look at half-tones of black on its own being used to achieve grey. Again with solids this is not a good idea, particularly with digital printing where colour consistency and banding can become challenging issues. The same principle as with printing black applies. Also, we see this a lot with business cards and flyers where the customer is looking for more economical printing alternatives while maintaining a visual impact. For these type of jobs you would be well advised to discuss the inherent risks upfront with the customer.