What is an API?
An application programming interface (API) is a particular set of rules (‘code’) and specifications that software programs can follow to communicate with each other. It serves as an interface between different software programs and facilitates their interaction, similar to the way the user interface facilitates interaction between humans and computers.
How is it used?
When and where is it used?
References
The Web API Checklist
StackOverflow Meaning of API
Wikipedia on API