The primary domain name is the one which shows up in the browser bar when you go to your website. You can have multiple domain names associated with your website (for marketing reasons, or because you've changed your domain name over time), but it may be important for you because of marketing or SEO to specify which one is primary.
Choosing your primary domain name is a two step process, but there are other things to consider as you do it.
First, login to HomeSwing and click on the Website section.
In the block around the website is an item titled "Add/Remove Addresses". Click on that.
Here you'll get a list of all the domain names which are associated with your website. You can add an address here, and you can specify which one is primary.
To specify the one which is primary, click on the "make primary" link next to the appropriate one you want to be primary.
In addition to being on the list, your domain name's DNS server and/or A records are correct.