Externalities are one type of market failure.
Market failure is inefficient allocations of resources and less than maximal utility in a 'laissez faire' economy. Governments intervene to prevent market failure:
Market failure refers to a whole range of free market foibles:
++ the emergence of monopoly powers
++ the occurrance of negative externalities (price mechanism does not account for social cost). It is called an externallity because it affects an unconsenting and external third party to the transaction. That third party is society at large.
++ the unability to provide public goods, because they are non-rival and non-exclusive.
++ excessive fluctuations in the business cycle. THis happens because people panic easily and get carried away spending.
++ I think that inequality in income distribution may represent a market failure, if it limits 'opportunity' but not if it creates 'rewards for effort' (not sure bout that one)
hope that helps, thats from Tim Riley's year 11 text book btw, if you want to chase it up