Basically, API simply allow applications to communicate with one another. Many people get confused thinking API is simply a type of database, but in reality it isn't a database at all but rather an access point to an app that can access a database.
Probably one of the best known examples of API is Google Maps which allows developers who need map functionality to simply connect and embed Google Maps on web and mobile applications. Another example is Amazon or eBay APIs which both allow developers to use the existing retail infrastructure to embed there services into e-commence websites.
As software applications realise specialising in a niche and connected to 'add-ons' is the best path to commercialisation, you will see API's continue grow in popularity and complexity.
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