Market production
In a general sense, market production refers to the production of a product or service which is intended for sale at a money-price in a market. The product or service in principle has to be tradable for money.
However, in national accounts the term has a more specific meaning. The reason is that many producing organizations exist in the economy which either do not produce for any distinct market, or which partly produce for the market, and partly don't. These are non-commercial or partly commercial organizations, which can be mainly self-funded, but not for profit, or mainly funded by sources other than their own revenue. Statisticians therefore have to define "market production" much more exactly, in order to be able to separate out market production in a consistent way, and distinguish it from non-market production. If they would be unable to do so, they would be unable to measure market production in a meaningful and consistent way.