“NOM” is short for Norma Oficial Mexicana (Official Mexican Standard) which are the official standards and regulations dictated by the Mexican Government.
The Tequila Regulatory Council (CRT) regulates production of NOMs for the industry and it specifically identifies that the spirit meets government standards to be classified as Tequila (much like a bottle of Champagne must meet certain standards in France.)
Since 1990 all 100% agave Tequila must have a NOM identifier on the bottle. The NOM number on the bottle indicates the distillery. In general the lower the NOM number (starting around 1100) the older the distillery.