This is a development from the regular CMYK colour process, used in a few computer printers (the ones who use 6 colors - CcMmY = 5 + black = 6) and by print shops (you know - the people that print your magazines, flyers and everything else that's nice and has colors
The idea of the CcMmYK system is to solve some of the weaknesses that exist in the CMYK system.
So what's the difference between CcMmYK and CMYK?
CMYK consists of Cyan, Magenta, Yellow and Black (Key color)
CcMmYK is essentially the same, but uses an extra cyan and an extra magenta tone. In effect, the cyan and magenta tones are about 50% desaturated - imagine mixing Cyan with 50% white (or, actually, translucent) material, and you've got it.
Why is this needed?
When trying to reproduce some colours with the original CMYK system colors - light green in particular - the distance between every "dot" of pigment became very large. This made the results less pretty, and looked horrible if there was a gradient between, say, a light green and a light red. By adding lighter Cyan and Magenta colors, the actual correctness of the gradient wouldn't be much more precise - but it was perceived that way, which really amounts to the same.