GADM is a spatial database of the location of the world's administrative areas (or adminstrative boundaries) for use in GIS and similar software. Administrative areas in this database are countries and lower level subdivisions such as provinces, departments, bibhag, bundeslander, daerah istimewa, fivondronana, krong, landsvæðun, opština, sous-préfectures, counties, and thana. GADM describes where these administrative areas are (the "spatial features"), and for each area it provides some attributes, such as the name and variant names.
The current version is 2.6 (July 2015). A much improved version 2.7 will be released in August.
Compared to Version 2.0, GADM Version 2.6 has more detailed data for Cameroon, Greece, Kyrgyzstan, Lebanon, Nepal, and Romania among other countries. The second level subdivision has now been mapped for all countries (see these maps by level of subdivision). The current version of GADM delimits 275,158 administrative areas.
The data are available as shapefile, ESRI geodatabase, RData, and Google Earth kmz format. Shapefiles can be used for most mapping and "GIS" software. You can download a free program such as Q-GIS or DIVA-GIS. The RData files can be used in R with the 'sp' package loaded.
You can download the data by country or for the whole whole world.