Jemima Kiss {media guardian} The Nutshell: A beginners’ guide to APIs does a better job than i will explaining APIs.
I never really saw the use for them back in my days in cryptography. But in a non portal mash up 2.0 world APIs are key to activity and sharing. Rather than reduce the brand impact they spread it further away from center, now all you have to decide is, is your model (sometimes a business model) clever enough to take advantage and exploit these opportunities that APIs bring.
Think of it this way. Is there online real estate in the Twitter home page? No. Its frontiers without front pages.