It's mostly about sending additional headers with the response which your Firebug-plugin plugin interprets and displays in its console. There are similar plugins for other languages, see e.g. http://www.firephp.org/ (that has does a few things that I believe FP does not, like let you emit pretty tables)
I don't believe you can get access to headers in Javascript so if you wanted to smuggle your log messages out that way you'd have to set some giant cookies or the addon would have to intrude on the rendered page and modify it -- these plugins do not.
This has also the advantage of embedding those log messages in non-HTML content, e.g. a JSON AJAX respnose or a generated image.
