API stands for Application Programming Interface. Simply put, an API is a messenger that allows two different applications to talk to each other and exchange data.
The Waiter Analogy
The easiest way to understand an API is to imagine it as a Waiter in a restaurant.

Waiter Illustration
1. You (Client): Sitting at the table and want to order food. You cannot go directly into the kitchen and cook it yourself.
2. Kitchen (Server): The place where food (data) is prepared. The chefs in the kitchen don't know who you are or what you want until someone tells them.
3. Waiter (API): You give your order to the waiter. The waiter takes the order to the kitchen. The kitchen prepares the food. The waiter brings the finished food back to you.
In the software world: