"administer" is a pretty far reaching term. You might do some or all of the following:
- ssh into the box to update code, change settings, start and stop services;
- edit text via "through the web" editing devices your site offers, which may or may not be secure depending on your setup (no reason not to)
- upload code to a server-hosted repository using a version control system (likely via an ssh tunnel)
- scp files from remote machines to the host, hopefully you won't elect to use insecure FTP
"ssh" is something of the workhorse in all this. Using ssh for remote access to the server, in tandem with using public key rather than a connection password, is a bog-standard secure way of interacting with a remote box. ssh makes it possible to do quick and secure file transfer, and version control system updates too.