Definition from Wikipedia:

“In computer programming, an application programming interface (API) is a set of subroutine definitions, communication protocols, and tools for building software. In general terms, it is a set of clearly defined methods of communication among various components. A good API makes it easier to develop a computer program by providing all the building blocks, which are then put together by the programmer.”

API allows your custom apps to source relevant data from Piwik PRO Analytics Suite without having to manually source data every time. For example: reporting dashboards, BI software, data warehouses, etc.

More about Piwik PRO Reporting API:
https://help.piwik.pro/support/getting-started/reporting-api/