How does gel electrophoresis work?

A solution of DNA molecules is placed in a gel. Because each DNA molecule is negatively charged, it can be pulled through the gel by an electric field. Small DNA molecules move more quickly through the gel than larger DNA molecules.

Here is the simple answer:

It basically rips the DNA into pieces and those pieces are placed into the gel. The gel has holes throughout the contaioner and allowing the DNA pieces to wiggle through. These are pulled by an electric potential (or voltage) that attracts the DNA pieces. The larger the piece of DNA the shorter distance it will travel through the gel.