I don't understand jsonp. 

I understand JSON. I don't understand JSONP. [Wikipedia][1] is the top search result for JSONP. It says *JSONP or "JSON with padding" is a JSON extension wherein a prefix is specified as an input argument of the call itself.*

Huh? What call? That doesn't make any sense to me. JSON is a data format. There's no call.

The [2nd search result][2] is from some guy named [Remy](http://stackoverflow.com/users/22617/remy-sharp), who writes *JSONP is script tag injection, passing the response from the server in to a user specified function*.

I can sort of understand that, but it's still not making any sense.

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What is JSONP, why was it created (what problem does it solve), and why would I use it? 

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**Addendum**: I've updated Wikipedia with a clearer and more thorough description of JSONP, based on jvenema's answer. Thanks, all. 

 [1]: http://en.wikipedia.org/wiki/JSON
 [2]: http://remysharp.com/2007/10/08/what-is-jsonp/