An API is an “application programming interface” which provides instructions for computer programs to interact with a database.
For example, you can get a forecast from the National Weather Service by going to Weather.Gov. But the NWS also offers a web service (known as an ‘Application Programming Interface’, or API) that allows external applications to access the NWS database in real-time. This enables developers to build applications that connect to the NWS ‘platform’ in order to seamlessly provide public weather data to skiiers, photographers, rainbow chasers, etc. (See this segment from John Oliver’s Last Week Tonight about the National Weather Service and the importance of open platforms for public information.)