Industry classification systems describe or define the structure and activity of a country's or region's economy, and use numeric codes to refer to these descriptions and definitions. For example, in the American NAICS system, there are the following codes for describing the aircraft engine industry, and showing how it fits into the broader economic picture:

336:	Transportation Equipment Manufacturing
3364:	Aerospace Product and Parts Manufacturing
336412:	Aircraft Engine and Engine Parts Manufacturing

The shorter codes, the three-digit code 336 in this example, are used to describe broad sectors of the economy. The longer codes are used to describe the more specific, narrow industries.

Industry classification systems are used to organize data collected by government agencies and commercial publishers about economic or business activity, and then to present that data, or in other words, to publish the data. The data are collected usually at the level of the establishment, not at the level of legal entities (a.k.a. companies or enterprises).

Usually it is governments or international bodies that create and maintain these classification systems.

Primary industry codes:

Designate the line of business (industry) from which the company derives the largest proportion of its income.

Secondary industry codes:

Designate any other lines of business from which the company derives income.

Implications:

The distinction between primary and secondary codes is sometimes artificial.  But it's helpful when looking at companies that are diversified:  a primary industry code let's you know how a company really makes its money. 

Let's look at GE (General Electric) as an example.  Although it may be best known for light-bulbs, here are NAICS codes for it in descending order, starting with its primary industry:
 –   335999 (all other miscellaneous electrical equipment and component manufacturing)
 –   551112 (offices of other holding companies)
 –   335121 (residential electric lighting fixture manufacturing)
 –   522298 (all other non-depository credit intermediation)
 –   515120 (television broadcasting)

(Taken from the GE company profile in Business Insights Essentials on August 31, 2022.)

Let's use McDonald's (the fast food chain) as an example:

An establishment is one particular McDonald's restaurant at one specific location.  In contrast, McDonald's the company (a.k.a. the enterprise) includes all of the restaurants, the corporate headquarters and any warehouses, research facilities, and so on.

An establishment is "the smallest operating entity for which records provide information on the cost of resources--materials, labor, and capital--employed to produce the units of output ... [The establishment] is generally a single physical location, where business is conducted or where services or industrial operations are performed (for example, a factory, mill, store, hotel, movie theater, mine, farm, airline terminal, sales office, warehouse, or central administrative office)."

 -- NAICS Desk Reference. Indianapolis, IN: JIST Works, Inc., 2000. p. xii.

For more detail on the history of industry classification, read chapter 3 in the 2001 Report on the American Workforce (Raynor Ref HD 5724 .R47); the three brief paragraphs below are drawn from it.

The US government began collecting industry data with the 1810 Census of Manufactures. But throughout the 19th century, there were huge problems with how data were collected and what data were collected. Clear industry definitions were not universally applied: therefore, for example, we do not know if "printers" meant the same thing to people in New York City as to people in San Francisco. As a result, government economic information at that time was very rudimentary.

During the mobilization for World War I, government officials realized how poor their economic information really was. They began to coordinate the collection of economic data by many government agencies, and began to develop a universal classification system, in other words a system of definitions, to make reliable analysis of the data possible. The Great Depression gave this endeavor a decisive impetus, as the government sought more and better information about the economy in order to prevent another collapse. One result was the Standard Industrial Classification System (SIC), first published in 1939/40.

The SIC contributed enormously to the quality and usefulness of government economic information, and it is still the most commonly used classification system.   Nonetheless, constant amendment has made it unwieldy; and economic change has undermined many of its categories. The creation of NAFTA generated the need for a new system capable of organizing data on the economies or the US, Canada and Mexico. The result is the North American Industry Classification System (NAICS), which will supplant the SIC in 2004, at least for data collected by the US government.