I had a really hard time understanding what an API was when I first learned about the concept but then I found this really brilliant metaphor.
API (Application Program Interface) APIs allow software to communicate with each other. One program can call on another program's API, thereby obtaining the data and functionality of this other program.
To break it down even further, consider this scenario:
In this case, Mary and Joan are the programs. The phone number that Mary sets up is the API that is used to pass information/data. The data in this case are the recipes that Mary has. If Joan decides that she wants to change up the recipe, she can do so as well i.e. manipulate the data that was provided.
Good right?! Hope it helps!