OpenID is a way of using your credentials on one website to sign into another. Imagine that you are surfing the web and find an interesting new site that you want to join, say www.newsite.com, normally you have to fill in a form with some personal information, you might use the same password that you always use, and click “join”. Retyping all your info is a pain but the real problem is that Newsite might not be very secure and your password and details are at risk. Much better, if Newsite allows (not all do) is to use an OpenID. What happens then is that Newsite sends you to OpenID service where you sign in and are then returned to Newsite, along with any details that you choose. This way you only have one password to remember (which you should make as strong as possible), one place to change your details and potentially better security (e.g. Google is probably safer than Newsite).
So, if you don’t have an OpenID yet, get one. However, you probably already do as accounts from Google, Yahoo, Flickr, WordPress and several others can be used. Check here for details.
Using your own domain is a step further which makes your OpenId the same as your website. This is nice but probably only for geeks. If you want to do this it turns out to be very simple, as the Lifehacker article explains.
Will I do it? Maybe, I will certainly have a look at it. Already, a quick look around the web gave a different way of doing the same thing, check MyOpenID for details.