After you register a domain, the Internet has to have a way to find your site. Most of the time, your web host will give you a pair of DNS servers to give to your registrar. The DNS servers show the world where your site is, much like a driveway connects a house to the main road.
For many years, domain providers have offered an alternative to DNS: domain forwarding. To set this up, all one has to do is input a web address of where they would like the name to go, such as a directory within an existing domain or perhaps a freely-hosted site on a subdomain.
Domain forwarding is a little bit easier to set up, but should not be used under any circumstances unless your host does not support DNS (mainly free hosts). Domain forwarding provides only a simple redirect to site visitors and search engines, whereas DNS gives you a faster direct connection. Forwarding will only send visitors to one place, but setting up DNS lets you have additional pages on your domain.
In real-world terms, think of DNS and domain forwarding as ways to get across a river. DNS is a long, wide bridge that will let anything and everything across quickly. Conversely, domain forwarding is a one-seat kayak. It well get you where you need to go, but with serious limitations.