Well, not really. The DNS is what allows your domain name to be used to connect to your website. It's a "big" subject, but the "short version" is that when you host a website at Dreamhost, or any other web hosting company, your website is assigned to an IP Address, so that other computers on the internet can "address" your website and exchange information (make requests for pages, and have pages sent back). DNS converts "somedomain.tld" to the proper IP address so your site can be found. You designate your DNS servers with the company where you registered your domain name (for sites hosted at Dreamhost, they should be set to ns1.dreamhost.com, ns2.dreamhost.com, and ns3.dreamhost.com). Once you have done this, and the change is distributed around the Internet, a web browser will be able to find "domain.com" on Dreamhost. Why typing "domain.com" takes you to "domain.com/home.html" is another matter, discussed below.
The webserver program running at your hosting company is what actually delivers your pages back over the internet to users by answering the requests of their web browser, or other program, communicating with them via the appropriate protocol (HTTP).
At Dreamhost, that webserver program is called Apache. Apache can be configured to respond to web browsers', and other programs', requests in various ways.
The various options that can be used are many, but one of the options that is setup by default on Dreamhost, is that if a request (like http://domain.com) does not contain the name of a "page" or file (such as "domain.com/home.html" - the "home.html" part of the URL is the "page" or file), it will look into the directory "domain.com" for certain "default" files, and deliver them "automatically" if they exist. There are several such "default" file names or pages that are recognized by the Apache configuration at Dreamhost, and "home.html" is one of them.
Therefore, when a browser asks for "http://domain.com", Apache sees that there is no request for a file or "page" and begins to work its way though the list of "default pages" it is configured to search for. As you can see from the link I provided, there are a "lot" of possible pages that could be found. The first such page it finds, in your case "home.html", it then delivers to the web browser. Under the default installation at Dreamhost, if Apache finds no files with the names in the list, it will simply present an index of the directory "domain.com", listing the names of all the files, and other directories, found there.
All this is a "simplified" version of what is involved, but hopefully it explains what is happening with your domain. Once you learn more, you can change some of this behavior, but for now, it is just important to make certain that the "opening" or "home" page of your website has one of these names, and that is the "right kind" of file (an .html file must contain .html code, etc.). In your case, on the current http://www.faerilyn.com/home.html, it does, as "home.html" is displayed whenever someone visits "faerilyn.com". All you have to do to have that page work the same way on Dreamhost, is to put the home.html file in the faerilyn.com directory on your webspace using an FTP progam, along with your other pages, and your pages will be ready to go.
Once you tell your registrar to switch your DNS from their DNS servers to Dreamhost's DNS servers, and the change has made its way across the internet (from a few minutes to several days - the amount of time will vary for various users) your site will be displayed from the Dreamhost servers.
If you want to "check" your site, or view it before the DNS update has been made at your domain registrar's or has been "distributed" through the internet, you can do so as described in this Dreamhost Wiki Article on Viewing your site before DNS changes.
You might find this Dreamhost Wiki Article on Building a Website a good place to start, or begin exploring further by visiting the Dreamhost Wiki Getting Started Category Page, and selecting other topics from there. Good Luck!