It is perhaps belaboring the point a bit, but a STANAG is NATO-speak for a STANdardization AGreement. There are many NATO STANAGS. These are normative documents that normalize equipment, doctrines, test procedures, etc. that have been agreed to by all member nations of NATO. These documents are intended to ensure standardization of equipment, testing protocols, tactical doctrines, etc, among NATO member nations.
STANAG 4172 pertains to 5.56 mm rifle ammunition to be used in individual and light support weapons. This document details the properties and requirements of 5.56 mm ammunition that can be submitted to NATO for consideration of adoption. You can read it here if you wish:
http://www.skytterlag2.no/filestore/Skytterlag/klepp-filarkiv/Div/556x45NATO.pdf
This document not only pertains to cartridge dimensions but also chamber dimensions for the 5.56 NATO chambered weapons. Many specifications for physical and technical performance of 5.56 NATO ammunition are precisely given, including accuracy requirements, minimal muzzle energy, chamber pressure, port pressure, trajectory, penetration capacity, primer sensitivity, action time, environmental resistance, fouling, smoke and flash, and bullet pull.
The exact nature of the projectiles is not specified except for some specific requirements for tracer ammunition and the following statement: Ammunition with all metal bullets shall be free from design features which render barrels unserviceable due to erosion in less than 5,000 rounds. Properly speaking, for a 5.56 mm cartridge to be a NATO round, it has first to have met all the requirements of this STANAG, then be submitted to NATO for testing and ratified by all member nations of NATO. The case head also has to be properly stamped with the NATO head stamp mark which is a cross or cross-hatch within a circle.
Only a few such 5.56 mm cartridges have actually been adopted by NATO. The most common is the 62 grain steel tip penetrator which NATO designates the SS109 and the US Army calls the M855. Member nations of NATO do utilize other cartridges that have not as yet been ratified by NATO within their armed services. A common example used by the US Army is the heavy projectile 77 grain MK262. A lot of such military grade 5.56 mm ammunition gets called "NATO" whether or not it has been adopted by NATO.