API (application programming interface)
Have you ever dreamed of controlling several systems from a single one? From SharePoint to be able to create and manage tickets in another system so everything is all in one place? API's make this possible.
An application programming interface (usually called by its acronym, an API) allows two applications to talk to each other. You can think of it kind of like going to a hotel. You perhaps present yourself at the reception and verify who you are, perhaps with a document, or a name and reservation number. They then give you a key that allows you to go to a specific room and to common areas.
API's allow us to do something similar in programming. You are probably used to going to your favorite web site or app and you click around and type to get information or update information. An API allows you to do the same actions, but from inside another application.
Imagine coming to my web site and I have a form for your Gmail username and password. Through Gmail's API I can present your username and password at the reception and receive a key. Then on my web page I can display your emails and even allow you to write and send emails. Or imagine when you do some other action on my site we want an email automatically to be sent on your behalf even without you typing. API's allow for this.
In the above example it would be irresponsible of me to get your username and password from you when all we need is the key. Other services often take care of this situation by presenting the user with a secure popup. You enter your username and password and you confirm that you want to give permission to my application to perform certain actions on your behalf. You may even wish to give me permission to perform only a subset of actions.
Each API is different and the application will provide documentation on how to approach and use it. API's power the modern web and make it possible for applications to talk with each other.