I still don't see how this prohibits sessions from being used by another browser. Maybe there is something obvious that I am missing. arhuman, can you please clarify this for me?

What information is used in the hash?

If the information in the hash is not directly tied to the browser (such as IP address, browser name), I don't see how a server can determine if the "incorrect" browser is requesting the session.

If only the session key and some private value is used in the hash, how does the server determine if the hashed value came from the browser that it was originally sent to or some other browser?