What Is It?
Domain names are the words you type into your browser to find a website (like http://www.PrimaryGoals.com). They are sold on a first-come, first-served basis from companies like GoDaddy, Register.com, and number of other companies called Registrars. Most commonly, multiple domain names refers to getting the .COM, .NET, .ORG, and both the singular and plural forms of a domain. (Yes, that can be 6 domains or more.)
Why should I care?
Buying multiple domain names increase the chance that somebody who wants to contact you will be successful in their attempts to do so. Imagine that you own YourFantasticSite.com (which was still available when I wrote this). You start building your site to make it valuable. Then, when you are not paying attention, somebody else buys YourFantasticSites.com (with an S at the end). Now, some people that you hope will go to your site will invariably go to the wrong address. How many times have you written down the name of a site, only to realize it needed an S, or you were not sure if it was a .COM or .ORG?
For an even more clear example, many people hoping to find information on the US Whitehouse entered the address for Whitehouse.COM. Unfortunately, the government page is actually at Whitehouse.GOV, and for a long time the .COM address was owned by somebody selling items that were inappropriate for minors.
How do I purchase multiple domains?
Purchase subsequent domains the same way you bought the first one — through your registrar.
Note: You can also set up these individual domains to have different starting points within your site, making one page link to another, thus increasing your own link-love. For example, compare PrimaryGoals.com and PrimaryGoals.org.