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.
In the United Nations System of National Accounts (UNSNA), market production includes all those producing units who sell most or all of their output at prices which are "economically significant" (i.e. at prices which influence how much producers are willing to supply, and how much purchasers wish to buy).
[1] For example, a school or a university would be a market producer if it charges fees which are based on their production costs, and which are sufficiently high to influence demand for their services.
The school or university would have to generate a definite operating surplus (profit) or loss.
The organizations in this category do not provide a financial gain (a source of income or profit) to the units which control or manage them.