Facebook api (Application Programming Interface) is the library provided by the facebook for the developers so that developers can access information, submit information by programming.
API can help lots of business to increase their sales by removing an extra effort to their prospective client by not filling out all the information over and over again
Making API calls directly to Facebook can improve the performance of your app, rather than proxying them through your own server.
Basically it is a platform for building application that are available to members of the social network of FB.