A positive externality is a good or service which benefits a 3rd party when it is consumed or produced. One example of a positive externality in production is passersby enjoying the smell of a coffee shop. They are not directly involved in the transaction as they are neither a consumer nor a producer, but they do derive utility from it.
A positive externality in production means that the Private Marginal Costs (PMC) are greater than the Social Marginal Costs (SMC), resulting in a level of production below the socially optimal level.