DNS, Domain Name System, is a simple way for people to navigate the internet. It is somewhat like using a telephone book. If you know a person's name you can look up their telephone number. The internet works just like this.
Every computer on the internet on an IP, Internet Protocol, address which is a series of numbers separated by periods, e.g. 22.214.171.124. When you log into the internet via your ISP, Internet Service Provider, you attached to the web through their computer which does have and IP. Your computer doesn't have an IP.
Domain Names came into being to help people get around the web by using letters rather than numbers. So when you came to these help pages, www.wise-old-man.com, you were actually connecting to my host's IP.
All domain names must have a host's DNS names associated with it. Once you have a domain name, i.e. register a domain name, and find a host, you must post your host's DNS name to your domain name by using your domain name manager at your registrant. If you don't like your host's service you can cancel your hosting with them, find a new host, and then change your DNS names to the new host's names.
This process of changing your DNS names is simple unless you have purchased a GeoCities premium account. GeoCities registers your domain name for you (if you don't have one already) but they don't tell you who is the registrant or how to access your domain name manager. You can get this information for them. To see how please go to Changing GeoCities DNS