If you are running a business, or even if it’s a ‘hobby’, you want to try and “tie in” everything with the name of the business or what you’re doing. This gives you an “entity” that all works together. Rather then having your business name, then a free “limited” email address that doesn’t match your business name or some horribly long web address to try and remember a domain name allows your to “tie it all together”. If someone remembers your business name and it matches the web address, then they’re going to be able to find you. And that can turn into increased sales/better exposure to your market plus more....
Also, if you just use a “free” email address, or the address with your ISP (Internet Service Provider) and you decide to change then you have to notify everyone of the new address. With a Domain Name you keep it for as long as you want and it renews every two years. No more “yourname@yourisp.com.au”, you can have ‘yourname@yourbusinessname.com.au’.