A shapefile, officially referred to as an ESRI Shapefile, is file format used by GIS (Geographical Information Systems) software. The U.S. Census Bureau uses shape files to visualize various data like U.S. ZIP codes, County and State borders, congressional districts, and more. We use these shapefiles to generate the tile set overlays designed to be used with custom Google Maps applications and mashups.
Find out more in this Wikipedia article about shapefiles.