A .prj file is a small companion file in the shapefile format that records the dataset's coordinate reference system (CRS). It holds a single Well-Known Text (WKT) definition describing the datum, ellipsoid, and — if projected — the projection and its parameters.
Why it matters
A shapefile's .shp stores raw coordinate numbers but says nothing about what those numbers mean. The .prj supplies that context. Without it, GIS software cannot know whether 500000, 4649776 are UTM meters, whether 2.29, 48.85 are WGS84 degrees, or what datum applies. Missing or wrong .prj files are one of the most common reasons layers fail to overlay correctly or land in the wrong part of the world.
A concrete example
A shapefile in WGS84 / UTM zone 31N (EPSG:32631) ships with a .prj beginning PROJCS["WGS_84_UTM_Zone_31N", GEOGCS["GCS_WGS_1984", .... If you delete that file, QGIS or ArcGIS will load the geometry with an unknown CRS and may place it nowhere near its true location, or refuse to reproject it.
Common pitfall
A .prj does not transform data — it only declares the CRS already implied by the coordinates. If the coordinates are UTM but someone writes a WGS84 geographic .prj, the file is now mislabeled and will plot incorrectly. Fixing a missing .prj means identifying the true CRS from the coordinate values and metadata, not guessing. Note also that the WKT in older Esri .prj files can be slightly non-standard, occasionally causing mismatches with EPSG-strict tools.