A SSH key removes the need for a physical password to log in to a remote machine via SSH. To generate an SSH key on the machine you are using to log in, (not the remote machine you wish to log into), use the following code in Terminal:
ssh-keygen -t rsa
You will have an option to select where to save the SSH key, and select a passphrase.
Once the SSH key has been generated it will need to be copied to the remote machine you want to log into using SSH. Replacing USERNAME with the correct username, HOSTNAME with the correct hostname, and PORT with the correct port number, (-p PORT can be omitted if using the standard port 22 for SSH), use the following code:
ssh-copy-id USERNAME@HOSTNAME -p PORT
Optionally the remote machine can be set up to only allow access using a SSH key and not via a password. On the remote machine enter the following code in Terminal to edit the OpenSSH configuration file:
sudo nano /etc/ssh/sshd_config
Make sure that the line that includes PermitRootLogin is set to either without-password or prohibit-password. If any changes are made to the configuration file then OpenSSH will need to be restarted using:
sudo service ssh restart
If you have encrypted the disk on the remote machine, you may still be prompted for the user password on first login.