I don't know why I consider it my job to get people to understand web technology. Perhaps it's because I can see how useful and interesting it is. Perhaps it's because of how frustrating I find it to see the level of discussion about technology stop at buzzwords. Anyway, motivation aside, I wrote a piece for Bookmachine in which I explain in detail what an API is.
Read it here. It contains a JSFiddle with some code which is editable, too, and commented. Don't hesitate to get in touch if it whets your appetite and you want to know more -- I'm happy to have lunch and explain it, line by line, if you're at all interested.