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The same simple idea is behind all those concepts: to modulize things. Start from wrapping code in functions, to OO, to MVC, this is all about modulization.
When the web application is no longer just a bunch of static pages, or something relatively static like shipping cart or a forum like this, it becomes too complex for things like CGI etc. Once again, people need to simplify what they are dealing with and the way they looking at the applicatin. MVC comes in.
Model can be simply understood as the data (could be database, a flat file, a set of XML's), or activities against the data (for example a query, or an upadte, an OO method against a dataset object, a SOAP call, a Java Enterprise Bean...)
View is the window for you to see the data and its transition.
You need something to glue your model and view together, or I would rather say to seperate them, but yet attached. Now here comes the controller. As you said, for a web application, this is where your requests got handled.
There are lots of challenges when you do web application in MVC way. My experience tells me that one of the biggest challenge is the cost. If you want to do everything right (everything MVC), with the tools you have now, the effort is hugh. No free lunch!
In reply to Re^3: The Model View Controller pattern in web applications