Analog is the only type of signal that is amplified if I'm not mistaken..
Super loud- did your just plug in your headphones? A line out is to send a signal to another device, such as an amp. Or in a car audio application, people convert the stock car stereos signal to a line out, then feed that into a signal processor or equalizer, then ultimately an amp.
I've taken pictures, hooking up a fiio e7 amp to the line out from my M8. The M8 is being fed the optical output from my Xbox One. So I effectively converted the digital stereo signal to analog, then sent that signal out to the Fiio. Why anyone would actually replicate what I've done i do not know (Hopefully you have a stellar desktop amp and not just a portable one like mine, because almost every other portable amp is inferior to what is integrated in the M8).