A pecuniary externality is any case where an economic actor causes a price change. This is in contrast to the more familiar positive externalities (when you get more good than you pay for) and negative externalities (where you get bad things that no one is held accountable for); moreover, whereas positive and negative externalities have an effect on the net utility of the economic system, pecuniary externalities do not; any loses from one party are balanced by the gains of another party.
As a simple example: imagine that I sell widgets. It costs me $80 to build a widget, and I sell them for $100 each. You decide to go into the widget market, and decide that in order to undercut me, you will produce widgets for $80, but sell them for $90.
- You are $10 better off for each widget that you sell.
- The customer is $10 better off when they buy a widget from you rather than me.
- I am $20 worse off for each widget that you sell.
Things balance perfectly; I am out $20, but your $10 plus the customer's $10 means that overall, the economy has not lost or gained any value.
Of course, things get much more complicated than this, and there is no small debate as to what constitutes a pecuniary externality vs. a 'real externality'. Real externalities are those which involve a good or service being provided or denied; for example, if I bought up all the raw-widget-making material and refused to sell any for less than $200 dollars, a lot of the people who would like a $100 widget will be denied the product.
But if the demand for widgets naturally rises to the point where all the widgets I can produce are bought at $200, that is a pecuniary externality again! In that case, all the people who would buy $100 widgets are balanced by the people who are getting all that extra value from widgets -- that is, if they are buying widgets at $200, and you are willing to pay only $100, they must be getting at least $100 more value from the widget than you are; the $100 of value you lose is balanced by the $100 of value they gain.
This all gets extremely muddy when you are talking not about widgets but about health care, housing, or education. These cases are particularly questionable because the basic model assumes that people can buy what they value -- that there is no one who needs a widget (or, say, housing), but cannot afford the lowest market price that meets their minimal needs.