Doing business nowadays (online or not) requires email — whether it's a way for customers to keep in touch, receiving invoices from distributors, or giving a quick memo to your employees.
Because it's how you communicate with so many people, they can come to associate you with your email address.
Having your business email associated with something free, like firstname.lastname@example.org, shares half of the branding with another company — in a way, you're advertising for Yahoo!'s email service every time you're reaching out to someone about your business. Not only that, using a free email account can give the impression your business is somewhat amateur and, true or not, that's not how you inspire confidence in visitors.
- Your business is serious enough that you have your own website and email.
- People are much more likely to remember your domain name and your email address.
- You're not advertising for another company
There are also some other lesser (but still legitimate) benefits to having a professional email address with your own domain name —the coolest of which is that you can create any email address you desire. Not only are you going to get a better name than email@example.com, but you can also come up with other memorable ways to create a brand.
For example, because Jim's the boss of his business, he could set up firstname.lastname@example.org (as well as jim@ or any other email name he wants). While it might not be a great idea for all businesses (engineering firms are notoriously more serious), it's great to have that kind of flexibility available.