You keep your PC running. Your PC regularly reports to the DynDNS servers that "I'm Raghunathan's computer, and I currently have IP xx.xx.xx.xx".

When you need to connect home, ask "the net" where Raghunathan.dyndns.org or Raghunathan.homeip.net or Raghunathan.kicks-ass.net and the request will then be forwarded to the DynDNS server (who owns the domain) and it will respond with the last IP your machine has reported in. Your laptop or whatever you travel around with will then connect to this IP number, and reach your PC that you left at home.

But it only works if you get a public IP when your computer logs in.

If you have a firewall at home, then you must drill a hole in this firewall, to allow external equipment to connect in through the firewall to the PC behind.

So DynDNS is just a normal DNS, but with the difference that they don't hard-code the translation from a computer name to an IP, but instead have an interface where your PC at home can report in and inform about the current IP. People around the world do not need to know that you use DynDNS. Their machines will still find your PC, since DynDNS owns the domain names you will get your PC bound to. So just asking for xx.kicks-ass.net will forward the request to DynDNS as the owner of "kicks.ass.net".