A file with .apr extension is an ESRI ArcView project file that contains project information for an ESRI project. These were used by ArcView 3.x and are not supported by the new (9.x and 10.x) versions of ArcGIS. ArcView 10 can, however, import APR files. ArcView is a Geographical Information System (GIS) that is used for creating, visualizing, analyzing, and managing geographic data. There are other file formats that are used by ESRI for storing data such as the popular ESRI ShapeFile (.shp). APR files can be opened with any text editor such as Microsoft Notepad and Notepad++.
APR File Format - More Information
APR files are stored to disc as plain text files that can be opened with any text editor for examination and editing.