An API (Application Programming Interface) is like a waiter in a restaurant. Just like how you tell the waiter what you want to eat, a program can use an API to talk to another program and ask it to do something for it.
For example, if you want to post a picture on Instagram from your phone, the Instagram app uses an API to talk to the Instagram servers and ask them to post your picture for you.
So, an API is like a special menu that only programs can use to order things from other programs.