There's a lot to branding your business in sync with your domain name and I'm just going to discuss a few key points that begin with the letter A.
Authority and Affinity
Being a brand authority now of days is having a powerful domain name. Powerful domain names are valuable because they are memorable and reflect your business as a leader in your industry. Like it or not we live in the age of information overload, and that's a good thing. As a kid I would ride my bike back and forth to the library trying to juggle a stack of books, knowledge and products from all over the world are now at anyone's finger tips from just about anywhere. How does a customer find, return to, or recommend your business in a sea of 1.7 billion websites all competing for the first page of Google? This is why your domain name matters.
Affinity is the sense of the natural path to your business, a relationship to or the path of the least resistance. If a customer has to remember your domain name or apply a silly extension, not only are they going to have a hard time getting back to you, it's even more difficult for them to refer your company to their contacts. Word of mouth is still a powerful tool in growing your business.
Here's a few great articles on the subject of branding and why your domain name matters: Spend Less on SEO, More on a Memorable Brand by Jamie Zoch and The True Cost of Your Domain Name by Chris Zuiker.
One point I would add to both of these articles is that not acquiring your matching domain name is leaving the door open for your competition to purchase it. Some companies have spent millions just to keep their competition from having them.