APIs help you extend your websites functionality to mobile apps. You could also earn money providing services to external services.
APIs or Abstract Programming Interfaces are how various apps communicate with one another. Today APIs have been an assential service for many businesses as each website/service depends on others (ex: payment).
An example of an API consumption would be payment. Assume you have an e-commerce store. You have a payment portal. The customer will add his credit/debig card information. This information we will have to send to a payment service which will withdraw the money from the customers account and deposit it in your bank. This communication is facilitated through APIs.
But why would you want to implement an api? You may require to have your mobile apps supporting platforms like Android and Apple/iOS. You may also have valluable information that others will be interested in. With an API, apps can automatically communicate with one another. Many times APIs come at a cost, so if you have some thing you can sell, its money for you!
I develop high quality, efficient, robust RESTful APIs powered by Ruby Grape Framework and a variety of others.