One thing we touched on briefly was the concept of an SSH agent.
When you SSH to a server (after setting up a key) and you're prompted for a passphrase, what you're actually doing is decrypting the private key part of your public-private key pair (the id_rsa file by default), so that it can be used to verify that you are who you say you are against the remote host. It can get tedious to do this each time you SSH to a server, especially if you're managing hundreds or thousands of constantly changing boxes.
That's where SSH agents come in. They're somewhere for your now-decrypted private key to live, once you've given it the passphrase, for the duration of your session.
Once you've got your private key loaded into your agent, the agent is then responsible for presenting the key to any servers you connect to, without...