During gel electrophoresis, restriction enzymes are used to cut dna into fragments. those fragments are then added into a well cut from a slab of gel. an electric field is passed through the gel, causing the fragments to migrate to the positively-charged terminal at the other end of the gel. the dna fragments separate into bands on the gel because

The dna fragments separate into bands on the gel because it changes the rate of which they move. The shorter the dna fragment the faster it moves. The negatively-charged fragments and the positively-charged fragments will react differently to the electric charge. These changes cause the dna fragments to split off. Like if you are holding hands with some one, but then you start walking at a much faster pace then the person you are holding hands with. Eventually you would not be able to hold each others hand and would break off from one another.