All traffic over the Internet is actually controlled by numeric addresser (IP addresses). Try for example entering 216.185.111.40 in your web browser and you will see that you connect to www.theplanet.com. A DNS or domain name server is simply a computer with software and databases that converts the alphanumeric address www.theplanet.com to the numeric IP address 216.185.111.40. DNS also communicate with each other to be able to respond to queries.
Your domain has to be registered in a DNS for it to be possible for other people and computers to reach it with the alphanumeric address. The DNS must also specify in its databases which IP address your web is on, and to which mail server your domain's email should be sent.