The basic idea is to look at certain loci (places) in the genome which are highly variable between people. About 10 to 15 of these loci are needed for a match, and the legal details differ between countries. A match between a sample and a suspect individual makes it extremely likely that the individual was the source of the sample. This evidence would then be the basis of the prosecution case for a crime. A similar analysis would show that a man was very likely the father of a child. This is really a modern way to do what was done with blood groups before DNA details could be analysed. The methods have been developed mainly by the work of Alec Jeffreys.