Most of the time that code is pulled together from dozens of files if you’re using any sort of software package to manage a site.
Looking at the code that’s actually output (the HTML you’re seeing) lets you see what’s going out to the world without all the logic included. Basically it’s the end product of a long process and sometimes that’s the best way to find problems without having to go through all the machinery.
IE added this as a response to most web developers defecting to firefox when firebug came out.
and your changes there aren’t saved to the server, if you reload the page, it goes back to the way it was. No one else would ever see your tweaks.