How do I set up/what is a Callback URL?

A callback URL is essentially an "answer" URL that comes as a result of a redirect. For example, if a request is made from your site that requires a redirect to a third-party site and another redirect back (like a "confirmation" page), the site displayed upon the second redirect would be the callback URL. Alertra has a perfect explanation of how this works:

Callback URLs Explained

There's another great example of this explained in this Stack Overflow thread:

What is a callback URL in relation to an API?

You should be able to set up a callback URL using a single IP address similar to the way you would host multiple sites on a single Linode. Using Apache, you can acheive this by configuring your virtual host file to listen for multiple domain requests:

Configure Name-based Virtual Hosts