To understand why we would use a DNA fingerprint, it's helpful to think why we use normal fingerprints to identify a person. Any two people you pick are going to have an enormous number of differences, pretty much everywhere if you look close enough. However, the fingerprint is one of the easiest parts of a person to look at and compare to another person. With DNA it's a similar concept. Any two people (besides identical twins) will have different sets of DNA, called genomes. But, the genome is really, really large so for a long time it wasn't possible to look at 2 whole genomes and compare them to see if 2 people are different. The idea of DNA fingerprinting is that you only look at a very small part of the DNA that you expect to be different to determine if 2 DNA samples come from the same person.

In a real sense, the DNA fingerprint achieved is a barcode for a person in that it uniquely identifies people.