Magazines are printed with the CMYK process. This uses cyan, magenta, yellow and black ink to make up the colours.

The original is either copied via filters or modified via digital software. The printed colours are semi-transparent allowing them to combine to create more colours.

e.g. something red will be printed with both magenta and yellow which will combine to create red. A red object will have no (or very little) cyan in it.

Although it is theoretically possible to create black with the three colours, in practice a black print is added to improve the image.

EDIT: Actually, this explains it better than me: