Why do I need this information?
If you are creating your own artwork for print then the chances of you producing a job that we can both be proud of are greatly enhanced if you actually understand what is going on. You can then make artwork judgements in a more informed manner and avoid ways of working that may detract from the quality of the finished job.

What is CMYK Print ? (often referred to as Process Colour, 4 Colour or Full Colour)
CMYK printing is a process whereby many coloured images are created on paper by applying varying amounts of the four primary inks. If you look closely at any full colour printing on paper you will usually see that it is made up of different coloured dots. Normally Cyan dots, Magenta dots, Yellow dots and Black dots. These are the 4 subtractive primary ink colours used in the four colour printing process and the reason dots are used is because printing presses cannot print shades of a colour. The amount of ink at a particular point is adjusted by changing the size of the dot at that point.
In this way green image areas can be made of cyan and yellow dots, brown from cyan, magenta and yellow dots, orange from magenta and yellow dots and so on. A strong red approximating to Pantone 485 would be made of 100% Magenta and 100% yellow. A burnt orange colour could be made with 90% yellow dots, 40% magenta and 20% black. This would normally be expressed as C0,M40,Y90,K20.
CMYK inks are transparent and they act like light filters in that they adjust the amount and colour of light reflected back at you from the paper. Imagine that you have four coloured sheets of transparent plastic - one for each CMYK colour. Lay the yellow sheet over the blue sheet and hold the two up to the sun and you have green.

The colour range of CMYK offset print.
Expressed in terms of a digitised system standard CMYK offset print is capable of rendering about 4 million colours. This is considerably less than the 16 million colours normally displayed on your computer monitor and hugely less than you can see in a photographic print or transparency, in fact even considerably less colours than you can get from your office inkjet.

Black is a special case - acheivable TAC and grey component replacement
In an ideal world we should not need black because black should result from printing C100,M100,Y100,K0. The physical reality of printing is that this will actually give you a dark brown colour. Black ink is also transparent and so if you print C100,M100,Y100,K100 you get an extremely strong black. C100,M100,Y100,K100 is said to have a TAC value of 400. TAC stands for Total Area Coverage, in this case 100+100+100+100=400. This colour is not normally acheivable in production because most press systems will struggle with it. There is just too much ink on the paper and this leads to various problems such as picking, trapping, scuffing, sheet curl and set-off. In practice most presses don't cope well with TAC values greater than 320. Limiting yourself to TAC300 when creating your artwork is a good idea.
In CMYK printing in general but especially when reproducing photographs using CMYK, how you handle black has great bearing in the quality of the finished job.
Consider two grey colours C10,M10,Y10,K0 and C0,M0,Y0,K10. Ideally, when printed these two colours should be identical since mixing cyan, magenta and yellow in equal amounts should result in grey. Both colours should be a pale grey but in reality only the second colour will give you a guaranteed grey. There are various reasons for this. Ink migration on the press is a fact of life and will cause the inks to mix slightly and become impure. Variations in dot gain between colours is a reality. How your grey area is positioned on the plate relative to other objects can effect our ability to maintain correct ink density. In any case no press ever made can mantain perfect ink density balance at all times in all conditions. All these factors and more besides mean it is impossible to control ink balance sufficiently to guarantee a perfect grey made of CMY. On the day you may actually get C9,M12,Y10,K0 which will be a pinkish warm grey and your eye will know it. Avoid this problem by making your grey using 10% black only. To your eye C0,M,0Y0,K10 and C0,M,0Y0,K12 are virtually indistinguishable.
This may seem like alot of waffle to illustrate a minor point but what you see from this example doesn't just apply to grey colours. It is the principle of grey component replacement or GCR. When Cyan, Magenta and Yellow are present in sort of equal amounts the grey they create can be replaced with a corresponding amount of black. The result is greater colour stability and much improved rendition of shadow detail in your pictures.
Most superficial explanations of CMYK printing will tell you that black is used to make stronger black colours. There is more to it than that. This is one of the reasons why first class colour scanning is still a highly skilled operation and we use this example to illustrate the fact that producing truly first class artwork for print involves much more in-depth knowledge than just creating something that looks good on your monitor or when printed to your inkjet.

How does my CMYK job end up on paper?
We take the artwork you send us and use it to create a postscript/PDF file. This file is then passed to a program called a "RIP" (Raster Image Processor) which interprets the postscript program and renders it to four very high resolution bitmaps - one for each CMYK colour. If you requested an online proof we will then render a series of four low res bitmaps which are combined into a single CMYK file for you to view. Assuming you approve your proof we then use the four high res bitmaps to make four printing plates. These are loaded onto the press in exact position to ensure the 4 colours print accurately over each other and the job is printed.

So that's all there is to it?
Not really. Offset Litho printing is a highly developed and long established technology. It brings together many disciplines including: Optics, Computers, Electronics, Physics, Precision Engineering, Polymers, Plastics, Chemistry, Metalurgy, Paper Making, etc., etc.. You could spend a lifetime working in print and you would never know everything - even about your own particular field.