The price mechanism is remarkably good at matching what people want with what gets produced. It is also, in specific and predictable situations, badly wrong. A factory that pollutes a river faces no bill for the damage, so it pollutes more than it should. That gap between what a market produces and what society would want it to produce is market failure.
Market failure
A situation where the market mechanism allocates resources inefficiently, producing too much or too little of a good.
Market failure does not mean the market has collapsed or that firms are losing money. It means resources are misallocated. Candidates who define it as a market that has stopped working almost never gain the mark.
Externalities
An externality is a cost or benefit that falls on someone who is neither the buyer nor the seller. Because that third party has no say in the transaction, their gain or loss never enters the price, and the market therefore misjudges how much to produce. Negative externalities, such as pollution or traffic congestion, mean the good is over-produced. Positive externalities, such as vaccination or education, mean it is under-produced.
Economists split every cost and benefit into parts. Private costs are paid by the person or firm carrying out the activity, such as a factory's spending on wages and materials. External costs fall on third parties, such as the illness caused by the factory's smoke. Social costs are the total of the two: social cost = private cost + external cost. Benefits divide the same way. Private benefits go to the buyer or seller, such as the satisfaction a student gets from education or the wage it later brings. External benefits go to third parties, such as the gain to employers and society from a better-educated workforce. Social benefits are the total: social benefit = private benefit + external benefit. A market only counts the private parts, which is why it gets the quantity wrong whenever there are external ones.
The phrase examiners are looking for is 'third party'. A cost the firm itself pays is a private cost, not an external one. Naming a specific example, such as noise affecting residents near an airport, converts a definition mark into a full answer.
Two related categories often appear alongside externalities. Merit goods, such as healthcare and education, are under-consumed because people underestimate the benefit to themselves. Demerit goods, such as tobacco, are over-consumed because people underestimate the harm. Both stem from imperfect information rather than from third-party effects, which is a distinction worth keeping clear. Public goods, such as street lighting and national defence, are non-rival and non-excludable, so nobody can be made to pay and the market provides none at all.
Monopoly is a further cause of market failure. A firm with no competitors can restrict supply and charge a higher price than a competitive market would, so consumers buy less than they would like and pay more for it. Resources are misallocated because too little of the good is produced, and the monopolist has less pressure to keep its costs down or improve its product. This is why governments regulate monopolies, block some mergers and try to keep markets open to new firms.
Why does a free market under-provide public goods?