Emacs supports editing files remotely, as a nice alternative to opening a new emacs session on your remote machine and sending the window over X11. This feature is called tramp.
It works seamlessly – just open a file as usual with
C-x C-f and then give the name of the remote file, including the host address – e.g.
C-x C-f /host.server.com:/home/bjm/myfile.org
Note the syntax, that the remote machine name is opened at the top level directory “/”.
You can then edit and save as normal.
It is useful to note that you can also do exactly the same thing to open remote directories in dired to browse, copy, rename and otherwise manage files on a remote machine.
As commenter Nagora points out, if your username is different on the remote machine, you should specify it like
C-x C-f /firstname.lastname@example.org:/home/bjm/myfile.org