GeoTIFF is a public domain metadata standard which allows georeferencing information to be embedded within a TIFF file. The potential additional information includes map projection, coordinate systems, ellipsoids, datums, and everything else necessary to establish the exact spatial reference for the file. The GeoTIFF format is fully compliant with TIFF 6.0, so software incapable of reading and interpreting the specialized metadata will still be able to open a GeoTIFF format file.
An alternative to the "inlined" TIFF geospatial metadata is the *.tfw World File sidecar file format which may sit in the same folder as the regular TIFF file to provide a subset of the functionality of the standard GeoTIFF described here.
History
The GeoTIFF format was originally created by Dr. Niles Ritter while he was working at the NASA Jet Propulsion Laboratory.
The reference implementation code was released mostly as public domain software with some parts under a permissive X license.