From what I'm reading, it's the equivalent of the Presenter in the Model View Presenter (MVP) architecture.
It does business logic, not store or display data. It create a separate layer independent of how or where data is stored or displayed. It only cares about inputs and outputs in any format. It could be used in a combination of the Observer, Adapter, and Façade patterns to be an interface for callbacks, a generic extension point of the code, and a decoupled entry point for any non UI or data-storage usage, respectively.
I assume it is called an Interactor because the View interacts with it to calculate values and refresh any displayed UI elements and it interacts with the Model objects to extract data. It could also interact with a database for CRUD operations, but I think that's mostly addressed in the Repository Pattern as that isn't really business logic.