Economists use the term externality to describe any time the price determined by a market doesn't reflect the true cost of an action. A positive externality is a good consequence that isn't taken into account.
An externality is an effect that an economic transaction has on a party who is not involved in the transaction. 
Externalities deter a market from producing the equilibrium quantity and price for a good for service. Externalities produce inefficiencies in markets and can eventually produce a market failure if not internalized in time.
A positive externality is something that enhances society as a whole. It results from an economic transaction that has positive external effects on others not party to the transaction.
One example of a positive externality is the market for education. The more education a person receives, the greater the social benefit since more educated people tend to be more enterprising, meaning they bring greater economic value to their community.
The social benefit (SD) of obtaining higher education is greater than that of the private benefit (D). Because individuals do not factor in the social benefit, they are only interested in the private benefit and therefore they purchase a level of education which is not socially optimal.
To increase the level of education, the government could offer an education subsidy which would lower the cost of education and encourage more people to obtain a higher level of education. This would close the gap between P1 and P2 and increase the output of higher education. Therefore the individuals could pay the same price before (accompanied by a subsidy) and the overall level of education would increase and maximize the social benefit.