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The Web Server Dispatcher is just the Apache Web Server (or equivalent) with a module (Adobe Dispatcher) to connect to AEM Publisher to retrieve and serve content.
The advantage is that the Rather than allowing users to directly connect, using a Web Server will build a cache of the content reducing load on the AEM Publisher. This is because the AEM Publisher dynamically builds the web pages at every request (even if they do not change). In addition, the Dispatcher can perform load balancing with multiple AEM Publishers. Finally SSL certificate management with the Apache is a well known and documented.
You may want to read the Adobe Dispatcher online documentation for further background.
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