Theoretically, routers have public IPs that change often and you have to buy something to make sure they don't.
In practice, this has only ever happened once to me when my router got hacked and I had to get firmware replaced. So while its a major issue if you have a huge site that needs to be reliable, if it is just a personal site it can be okay to just assume it will never change, and if it does you can always just get your domain name to point to the new IP.
It may be worth it to look into something to make it more stable, but right now it just isn't worth the extra fee.