Most home internet connections have a dynamic IP, meaning it changes frequently (as often as daily or weekly).
Dynamic DNS is an internet service that sets up a domain (like rasczak.dynamic.com) and makes sure the public DNS for that domain always points to your home's current dynamic IP.
People want this if they want to remote into the home machine while they are not at home (cafe, library, work, friend's house). They also sometimes want this because they have a VPN at home and want to tunnel sensitive traffic through their secure VPN while they are away from home (some do this to bypass work proxies or filters). Another reason to do this is if you are running some type of server at home, like an FTP, or a web server or something.