DNS is the system the Internet uses to map hostnames (eg www.yourname.com to Internet address - 203.234.3.100).
This system means that humans can use easy to remember addresses (www.yourname.com) to access resources on the Internet rather than computer addresses (203.234.3.100)
To have your domain name setup in DNS you typically need to assign (or delegate) your domain name to a pair of "Name Servers".
These are computers operated by registrars and hosting companies to hold DNS information about your domain name.
Once your domain name is delegated users on the internet all around the world will be able to look up information about your domain name, as well as sending you email and viewing your web site.