What is electrophoresis? why does it allow scientists to separate pieces of dna?

Genetic fingerprinting – the analysis of DNA in order to identify the individual from which the DNA was taken to establish the genetic relatedness of individuals. It is now commonly used in forensic science (for example to identify someone from a blood sample) and to determine whether individuals of endangered species in captivity have been bred or captured from the wild. 
•DNA sequencing – the determination of the precise sequence of nucleotides in a sample of DNA or even a whole genome e.g. the Human Genome Project. 

The process of electrophoresis: 
DNA is chopped, close to the VNTR regions, into fragments using restriction enzymes. The DNA fragments are placed on the agarose gel and a direct current is applied continuously to the gel. The DNA fragments are attracted to the anode. The shorter the fragment, the faster it moves. 
The fragments are transferred onto an absorbent paper placed on top of the gel. The paper is heated to separate the 2 strands in each DNA molecule. Complementary probes which have a radioactive phosphorus isotope are and this pair up with the DNA strands. The paper is placed on an X-ray film and the film goes dark due to radiation emitted by the probes. Now we end up with a pattern of dark stripes on the film matching the positions reached by the fragments in the agarose gel.