ESRI:

A GIS stores information about the world as a collection of thematic layers that can be linked together by geography. This simple but extremely powerful and versatile concept has proven invaluable for solving many real-world problems from tracking delivery vehicles, to recording details of planning applications, to modeling global atmospheric circulation.

GIS - An Analogy, ESRI Canada

How Does a GIS Work?, USGS

An Introduction to GIS, The Geography Mining Co.

A very readable explanation of what a GIS means for a city