The National Stock Number, or an NSN as it's called, is a number used by the federal government to order parts. It consists of three parts, in the form of xxxx-yy-zzz-zzzz . The first part is called the Federal Supply Code, and it consists of two parts - the first two numbers represent a general category, which could be anything from office supplies to nuclear ordnance, and the second two numbers represent a subcategory - pens and paper, or uranium and shell casings. The next part is the NCB number, standing for the National Codification Bureau number. This is either 00 or 01 for items from manufacturers within the US, or 11-99 for items that are made outside the US. The final seven digits are randomly assigned as items are added to the system.
Why is this important?
Well, in the sense of E2, it's not. In the sense of the US government, it is. In any piece of equipment, you've got hundreds, thousands, or tens of thousands of little parts that make these things up, each of which could be from any number of manufacturers, or multiple manufacturers for the same part.
When you're looking up one of these parts, say... an integrated circuit chip, it's easier to list a single, 13-digit number than it is to list a part number, a manufacturer, and contact information for said manufacturer of the chip. A technical manual for a piece of equipment seems to average a couple of inches thick, and this would only be made worse by adding in all of this extra information. To look up an NSN, you first find the location of the item within the piece of equipment on which you are working. To give an example, we'll say that we're looking up an alternator for a vehicle. We look at the diagrams provided, and find that it has a number on it. We look at a list after the diagram, find the number, and we're given a part number. At the end of each TM, there's a list cross-referencing the part number with the NSN. It's a terribly inefficient system, but it's useful, since not all parts are given NSNs, and some NSNs are outdated, no longer having parts associated with them. Of course, when you can't find an NSN to go with a part number, you've got to go through a whole new fiasco.
Source for this writeup is my own personal experience with researching parts for the military. Blargh.