Well this is an interesting feature. Mozilla, like all browser vendors, has been constantly enhancing their web development tools. They are quite impressive, allowing anyone to debug any page, including WebGL shader replacement, audio network manipulation, and injecting Javascript, HTML, and CSS at run time. Firefox OS and Firefox for Android developers were even able to remotely connect to a desktop Firefox browser as if it were an IDE (which it really is these days). Today, Mozilla announced (via their Hacks blog) early support for remote debugging Safari on iOS and Google Chrome on Android.
The currently supported tools are: "Inspector", which allows searching, modifying, and injecting HTML and CSS; "Debugger", which debugs and injects Javascript; and "Console", which displays console output from the open tab and executes individual Javascript statements (which can be multi-line with shift + enter). You cannot, for instance, modify individual draw calls on a running 3D game, like you can with the same tools when manipulating a Firefox tab, but this is still pretty impressive for cross-vendor.
Remote Debugging for Safari on iOS and Chrome on Android is available in early development on Firefox Nightly with an optional extension.
