False easting and false northing are fixed constants added to the x (easting) and y (northing) values of a projected coordinate system. Their purpose is to shift the origin so that every coordinate within the projection's area of use is a positive number, which simplifies storage, sorting, and human reading of coordinates.
Why it matters
Without these offsets, a projection centered on its origin would produce negative coordinates on one side. Negative values are error-prone in field notes, databases, and legacy software. By moving the apparent origin far to the southwest of the real one, false easting/northing guarantee positive values across the whole zone — a practical convention rather than a change to the underlying geometry.
Concrete example
In UTM, the central meridian of each zone is assigned a false easting of 500,000 m. A point exactly on the central meridian therefore has an easting of 500,000, points west of it have smaller values, and points east larger — all positive because the zone is only 6° wide. The false northing is 0 m in the northern hemisphere but 10,000,000 m in the southern hemisphere, so that the equator does not produce negative northings as you move south.
These values are part of the CRS definition stored in an EPSG record or a .prj file (the false_easting and false_northing parameters in WKT).
Common pitfall
Mixing up hemispheres — applying a northern-hemisphere false northing (0) to southern-hemisphere data — shifts every point by 10,000,000 m. Likewise, tools that report "raw" projected coordinates without the offset will appear to disagree with standard UTM values. Always trust the CRS definition, not a manual offset.