An externality refers to the impacts of a transaction on bystanders not partaking in it, including one-party production of a good. An example of a negative externality might be the lower surrounding air quality for other people when person A burns wood for heat. (To the extent that person A also experiences the lower air quality, it is negative, but not an externality.) An example of a positive externality would be if person A instead produced wonderful smells for a personal project that surrounding people enjoyed.
The presence of externalities poses problems for social utility optimization, as it then may not be enough for agents to simply do what improves things for them and those they transact with. There may be cases where the loss of utility from externalities vastly exceeds the benefit to the primary parties, and so it would be desirable to have a mechanism whereby such parties have an incentive not to do the action in those cases. Oppositely, there may be things that aren't done at all, even though the positive externalities would far exceed their production costs.
Often people will try to coordinate so that they can collectively benefit from provision of that good and ensure that the provider is paid, but often times, the coordination or transaction costs are so high that they are left at socially suboptimal state.