Digital Storytelling is the modern expression of the ancient art of storytelling. Digital stories derive their power by weaving images, music, narrative and voice together, thereby giving deep dimension and vivid color to characters, situations, experiences, and insights. - Digital Storytelling Association
The above quote was taken from a comprehensive website on digital storytelling http://electronicportfolios.org/digistory/. This website includes examples as to the many ways in which digital storytelling is utilized in Education, provides tools for creating and publishing digital stories, as well as international digital storytelling resources.
In my own words, a digital story is a short (usually five minutes or less) digital video clip which includes voice narration of a story accompanied by illustrations and/or still images and background music to add tone and feeling to the story. To see a digital story (less than 3 minutes in length) about how to make a digital story, go to http://www.youtube.com/watch?v=LknwS15wSx8.