Just gone thru, the listed message showing the difference between and an appserver and a webserver but still the picture is not very clearer.
So required more specific and to the point differences between both of them.
The web server services the web requests and formats the output sent to the client.
The app server takes care of the business, gets data from database, handles business rules and then supplies the processed data to the web server.
Often the web server and the app server can be on the same machine, but it is still a good idea to separate the concern of processing data from the concern of processing requests and generating output. It makes it easier to maintain and extend if each separate concern is in its own place.
One way, then, when your single server is no longer enough, you can put the web server and the app server on different machines to get "double" the processing power.
Another way would be to just cluster your single server model on two machines, but this might still have some problems even if the technique is evolving rapidly (see IBM's latest ECPerf)
Hope this answers some of your question
Simply put...the web server handles typically static files (html, images, etc.). The app server is meant to service dynamic requests (business logic, etc.).