In ArcGIS: Shapefiles can be added directly to ArcMap or ArcCatalog. They consist of multiple files (.shp, .shx, .dbf, etc.) that should be kept together in the same folder.
In QGIS: Shapefiles can be added by dragging and dropping the .shp file into QGIS or by using the "Add Vector Layer" tool. QGIS natively supports Shapefiles.