If you want access to your home server or computer or whatever at home, whilst not at home, it's useful. Saves remembering IPs and avoids the issue of the IP changing if it's dynamic.
If you own your own domain you can use a free service like afraid freedns to run the dns for your domain, then add a subdomain that points to your home IP. You can then also update that dynamically to reflect IP changes.
I think there's other similar services available but afraid worked fine for me so didn't try others.
So you could have
smiffy.com pointing at your website
home.smiffy.com pointing at your home server
They don't have a client application to update for you, but they do provide a Restful HTTP API and SDKs for PHP, Python, Go, JavaScript and a few more if you also fancy a coding challenge.
