API

An API (Application Programming Interface) is a software interface that lets one piece of software or service « connect » to another in order to exchange data and features.

APIs unlock many possibilities: data portability, email marketing campaigns, affiliate programmes, embedding features from one site into another, or open data. They can be free or paid. Source: cnil.fr

Example: when you use an app on your phone, the app connects to the internet and sends data to a server. The server fetches that data, interprets it, performs the required actions and sends data back to your phone. The app then interprets the response and displays the requested information in a readable form. That is exactly what an API is for: the whole process goes through it.