Possible uses for your computer could be:
- a web server to host your site or blog
- an image server to share all your travel photos
- an FTP server to allow access to files remotely
- VNC server to allow remote control of the computer
- a music streaming server
But services like DynDNS and No-IP solve that problem for you. They provide a static URL of your choice (limited to certain extensions) that gets mapped to your dynamic IP. By installing a small client on your computer (or, in the case of some routers, by enabling an option in the router configuration) the server gets notified every time the IP changes, and updates a DNS (Domain Name Server) accordingly.
I use both services (one on my Mac, one on the PC) and use the free service in both (it has a nag feature, where every 60 days you get notified that the service will expire unless you login within 24 hours and verify your address) - the premium service, with more available address, shorter TTL and extra features costs $9.95/year.