What is externality in economics?

Externality is a economic side-effect. Externalities are costs or benefits arising from an economic activity that affect somebody other than the people engaged in the economic activity and are not reflected fully in prices .
For example smoke pumped out by a factory may impose clean-up costs on nearby residents; bees kept to produce honey may pollinate plants belonging to a nearby farmer, thus boosting his crop.
Because these costs and benefits do not form part of the calculations of the people deciding whether to go ahead with the economic activity they are a form of market failure.