Working as a professional within the GIS discipline, I often find it challenging to describe to people what GIS is (in a face to face conversation). Telling them that GIS stands for Geographic Information Systems, which encompasses a set of technologies that can be used to analyze, map, and organize spatial data is a bit over most people heads. On the contrary, telling people that GIS can be used to make maps on a computer falls far short of its many potential uses. With this, I'm looking for some effective video examples that one could show somebody that explain both in words and visually what GIS is, and how the technology is utilized (something your Mom could understand :))?
I love the Geospatial Revolution series of videos from Penn State University.
It's a beautifully produced set of videos showcasing some everyday uses of GIS.
What is GIS by ESRI: Short and informative, with understandable images and use cases, and a groovy introduction music. Otherwise, just say: "GIS technology is kind of like Google Earth, but beeetter".
Perhaps it doesn't show exactly the current state of GIS (at least it doesn't look like that in my organisation so far ;]) but I really enjoyed video from Pacific Northwest National Laboratory on Precision Information Environments. Quite a lot what is happening there is either directly or indirectly related to geospatial technologies (of the future). (via @IJHGeo)
For more rigorous approach to definitions and concepts have a look at Defining a GIS: Essential GIS functions from users presentation from FOSS4G2011 conference.
Also see https://www.youtube.com/watch?v=wDVNBDIVUZo -it explains what it is, what people do and what the world would be without it.
I am working on one for aboriginal children. See https://gis.stackexchange.com/questions/112545/what-is-gis-for-indigenous-peoples
And it's only 1 minute long, so you won't lose their attention.
Video link available at: http://video.esri.com/watch/3623/what-is-gis_question_