Imagine you want to quickly change a directory path in httpd.conf, instead of downloading the file, editing and then uploading it via FTP - just nano that sumbitch and you're done.
I learn how to use it in about 30 minutes. That's really all it takes to get the basics down.
C-x C-f /ssh:user@host:/path/to/httpd.conf
... and I have it open in my local emacs, with my own settings, with colour and indenting, and no lag when I'm editing. (this is called tramp mode)
And if I then typed M-x eshell, I'd have a shell at the directory where I opened that file, and the nano users would start shouting 'burn the witch!'.
Other editors also support remote editing over ssh - no need to download/upload, the editor takes care of that for you. Working this way, I don't even have to trust that the remote server has nano or emacs or whatever - which it often doesn't.