Typically, though, if the browser could display some kind of information on the nature of the error, this could give a savvy user something they could type into a search engine or ask an intelligent question about on a forum, which might help them fix whatever is causing their problem.

This might not apply as much to the web, where the problem is likely a malfunctioning network connection, or a problem with the web server (or server side code). But it could help where the user is having a problem trying to accomplish something with an application which they will never be able to do until they change something on their end, or attempt it a different way.