The domain name system (DNS) enables each machine connected on the Internet to be recognized by a domain name. Every computer on the Internet has a unique IP (Internet protocol) address which consists of a string of numbers. Since the IP addresses can be difficult to remember, the DNS allows a familiar string of letters (the "domain name") to be used instead of the IP address. So instead of typing the IP address' you can type, for example, "www.microsoft.com."
Quick 'n Easy Mail Server needs a valid DNS server address to request to matching server for a specific email address, so it can deliver the messages for this address to the right mail server.
Usually your ISP provides a DNS server IP address which you can use for this purpose.