Here is a video that explains very well, although somewhat more advanced than in the previous video (video above =What is Web 2.0) ?, Does the term "mashup" mean and what are the API (application programming interface).
The only obstacle that must be overcome to understand this video is English David Berlind of ZDNet ... it's not that complicated, if not that the problem is that it speaks fast, so you have to concentrate and be very careful.
The video is 3 years but examples are still valid and clearly illustrate the concept.
By the way, if you want to know why companies open their source code, and create the APIs that third parties connecten seek their services, you are interested in this article What is a Network Metcalfe?
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