A private API is an application programming interface that has its application hosted with in-house developers. Private APIs act as front end interfaces to back end data and application functions. The interface provides a point of entry for developers or contractors that are working to develop those functions. These developers create an API to interface with the application that itself is running in-house for their employer or client.
One example of a private API is Home-Cost, a home building cost calculator. Home-Cost is provided as a customized installation for each client. The API might be made available through a home building supply store, enabling customers to pick the supplies to complete their projects with running tallies of costs.
Private API contrasts with a public API, which is a service offered by a party who provides outside access to internal resources. EBay is one example of a public API interface. The service, in this case, is a platform from which to buy and sell goods. EBay has also built a series of APIs around the core API to enhance functionality for buyer and seller alike.