Page Scope is the smallest scope, and is a representation of the PageContext object for your JSP. Each JSP has it's own page scope, so objects in the page scope of one JSP are not accessible to other JSPs. This is sorta like making a private variable in Java.
Request scope is the next smallest scope, and is represented with the JSP's request object. All JSPs and servlets that share a request share the request scope. For example, if I have a JSP that forwards to another page, and that second page includes a third JSP page, then all three pages are in the same request, and can share objects through the request scope. A special note here, is the response.redirect(), will create a new request, unlike forwards and includes. Also note, a new request is made every time the user gets a new page, be it by clicking a link, a button, or some JavaScript call.
Session scope is the next lowest scope, represented by an HttpSession object. All requests from the same user are in the same session (unless you or they make it otherwise). Each user has his own session. If you want data to be referred to through multiple pages, after each page is displayed and the user requests a new page, then store the information in the session. Note, in order for sessions ot work, the user must have cookies on, or you must re-write the URLs. Take a look for maintaining sessions for more help on that.
The widest scope is the application scope, represented by the ServletContext object. All users share the same values of the application scope, as there is only one made for the web application. If you have some static material that all users should be able to access, then put it in the application, but be carefull. Each user will see the changes other users make, and certain threading issues can occur if not handled properly. So application scope is usually best used for Read-Only data.
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