Request - Normally used for passing data from jsp to your servlet when you submit the form. When you get redirected to another jsp, your request dies. ie: this attribute lives per user request.please note that http is stateless protocol.so the server will treat every http request as a new request.
Session -session object is basically used to store the values in the session.the data will be preserved until the user terminates the program or closes the browser.Good example will be for storing user credentials. once user is authenticated, Sometimes you may want to check if the user has right access to do on some database operations like add/delete/edit. Once user closes the browser or the session goes idle for x amount minutes (depending on your server setup), the session dies and all info in it will be gone.
Context -context object can be used for multiple users and across multiple browsers.
If it is application specific, consider using context.
If it is user specific, consider using session.
If it is request specific (ex: jsp form submission), consider using request.
Hope this helps.