An API is an acronym for Application Programming Interface which means communication between multiple software. Don't be scared, Let me break it down.
Basically, An API enables you to have access to a website's/software's data (like spotify, twitter and so on).
How, you may ask? It gives you a nice user-friendly way to read and write data to and from another website's database.
Where to get a websites API from?
APIs are usually located at the footer of a webpage and usually anchored as developer. Go to Last.fm and navigate to the bottom and thats a real world api.
APIs ain't really scary, they are just here to make our lives better, and to enable us use rich datas without having to create and write them ourselves.