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Application Program Interface

A set of routines, protocols, and tools for building software applications

Practically, an API is any interface that enables one program to use facilities provided by another

A good API makes it easier to develop a program by providing all the building blocks

Check these sites for great APIs and some good tutorials:

http://nate.koechley.com/blog/2005/01/20/beautiful-api/

http://www.flickr.com/services/api/

http://www.programmableweb.com/apis