Dynamic DNS or DDNS is a method of updating, in real time, a DNS to point to a changing IP address on the Internet. This is used to provide a persistent domain name for a resource that may change location on the network.
Many routers have built in DDNS Services but can be limited in the services which they update. If the Router supports a the service, or you are willing to pay or donate for a service, you should do this, it is faster and more reliable. In that case, there is no need to use a softwareside solution.
Software Dynamic DNS
FreeDNS.afraid.org is a free Service which is easy and uncomplicated to set up.
DynDNS is another Dynamic DNS service.