The P/N is the NSN, or National Stock Number. The first 4 are the FSC (Federal Supply Code). Of the FSC, the first 2 digits identify the category, and the next 2 identify the class within the category. The next two digits identify the country of origin (00 and 01 show US made products). The next three identify the manufacturer, and the last 4 are the part number. Although it is more like the last 7 identify the manufacturer and part number together. Different sizes from the same manufacturer generally have the same 3 digit identifier and different last 4s. Manufacturers who make a metric ton of different parts, or have been in business since Christ was a Corporal may have multiple 3-digit identifiers as well. Not sure if vendors can share one identifier across a couple of vendors.
Oh, and just to get confusing, the identifier is based on the first brand contracted. For example, acetaminophen, which is bought from a bunch of different manufacturers, it's ordered based on one NSN, and whatever brand is cheapest is what you get. The NSN may be for the Tylenol brand, but you get what you get.
The nomenclature box has the descriptor that you can use to order the set through unit supply channels. It's fairly important to make sure the nomenclature matches the NSN, or it's dealer's choice if you get tthe thing you ordered by NSN, or the nomenclature item. Usually which ever one you didn't actually want / need. I.e., if you put in the descriptor for aspirin but the NSN for band-aids, you might get one or the other, or your order might get cancelled with no notice or warning, and there is no way to predict the outcome, and attempting to observe the decision process may change the outcome. Schroedinger's Bandages.
tl;dr: It's basically a pick ticket for inventory management.