Lets say you are developing a game and you want the game user to login their facebook profile(to get your profile information) before playing it,so how your game is going to access facebook?
Now here comes the API.Facebook has already written the program(API) for you to do it, you have to just use those programs in your game application.using Facebook-API you can use their services in your application.Here is a good and detailed look on API...
http://money.howstuffworks.com/business-communications/how-to-leverage-an-api-for-conferencing1.htm
