In the context of application integration interfaces, there isn't a universally accepted term like "parent." However, depending on the specific scenario, a couple of concepts might be relevant:

1. Integration Platform:  This could be considered a parent in some situations. An integration platform like an Enterprise Application Integration (EAI) platform or an Integration Platform as a Service (iPaaS)  provides the environment and tools for building and managing application integrations.  Different applications can connect through pre-built connectors or utilize the platform's capabilities to develop custom integrations.  In this sense, the platform acts as a central hub facilitating communication between various applications (children).

2. Source Application (for Data Integration):  For data integration scenarios, the application that provides the initial data source could be seen as a parent. This application might expose its data through an API or another interface, and other applications (consumers) would utilize that data.  However, this is a looser relationship compared to the integration platform example.

It's important to understand the context of the discussion to determine the intended meaning of "parent" in application integration interfaces. If you can provide more details about the specific scenario where you encountered this term, I might be able to give a more precise explanation.