API (Application Programming Interface) is a powerful way for applications to make data available to other applications. For example, Google Maps has an API that allows anyone to use data and features of Google Maps in their own applications.
While API is not something that even a UX Engineer might touch directly, it is important for UX designers to understand implications of getting data from API, such as delays in response, or limits on number of records that can be sent and received at once. It is best to work with the development team to understand and resolve those issues as they might impact the user experience of the application.