An externality is a cost or a benefit that is not included in the market price of some good or service. There can be positive and negative externalities.
Negative externalities are the more familiar of these. An important negative externality is pollution. For example, let us assume that burning gasoline contributes to global warming and global warming will incur costs on us in the future. In that case, the costs of dealing with global warming ought to be included in the price of gas. But they are not. That makes this a negative externality.
Positive externalities exist, for example, when benefits come to people who did not pay for them. For example, imagine that I go to college and become educated. My family and I pay my way, but my education ends up benefitting society as a whole. I use my education to teach other people's kids, but they do not directly pay for the education that I got.