Why we use bits of DNA that have little known function to do DNA fingerprinting?

The simplest way to explain this is to first have a look at the parts of our DNA that DO have known functions.

Logically we can assume that if a section of DNA that has an important function then we don’t want the sequence of that region to vary much, otherwise the encoded instructions would get scrambled and the DNA would lose it’s function - often leading to disease. For example, pretty much everyone has the same DNA sequence to produce hemoglobin (the oxygen carrying protein in your blood) since every single human needs it to be functional in exactly the same way.
Now DNA fingerprinting is only useful if it examines regions of our genome that DO vary a lot between individuals, and hence these regions tend not to be those that encode essential functions.