According to the first article I have attached, the noncoding sections are what ARE important in DNA fingerprinting. DNA is extremely long; the number of base pairs on the chromosomes of humans is about 6 billion in each cell. Non-coding sections are just what they sound like--sections of DNA that are not being transcribed/utilized by the organism. They make up a huge percentage of the total, somewhere between 95 and 98 percent. Because they do not actually end up being transcribed by the organism, mistakes such as duplications are "not under great selective pressure and are prone to variation; mutation rates and crossovers within these sites are high" (ncsu.edu link below). They therefore tend to vary more from individual to individual, and are of great use in identifying who the sample came from. Researchers have managed to choose sections of the DNA that are most variable between individuals in order to identify them. This technology is also used on organisms other than humans.
The third article attached below concerns a different type of analysis, of sections of DNA that do code for characteristics. It is being used to try to figure out such things as eye and hair color from an unknown, criminal source.