This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
If you get the RequestDispatcher from the ServletContext then you cannot use a relative path (no / at the beginning of the path) because that would mean that you are saying to locate the resource relative to youself which is the ServltContext. Relative to yourself has no meaning. This is why you use the / at the beeginning of the path.
If you get a RequestDispatcher from your servlet, then the idea of relative to yourself means where on the file system the servlet is located and you can indicate a resource relative to yourself (no / at the beginning of the resource path) or relative to the web app (Context root) by starting the repurce path with a /.