1. Taking control of your email.
How many people do we know with bizarre email addresses, like firstname.lastname@example.org? You know instantly that the name they tried first was already taken. This is becoming more and more common as the number of people on the internet increases. In 2005 there were 1 billion internet users world wide or ~16% of the worlds population. in 2016 it's estimated that over 46% of the world is on the internet, nearly 3.5 billion people. It's remarkable growth, but there's another 4 billion people to go. Having your own domain name means you don't have to get lost in the billions of other users using the most popular mail services, gmail, hotmail / live etc. You can still use the services, but you will have your own, unique domain to identify your mail with.
2. Don't be tied down to your ISP (Internet Service Provider)
I have family who's email is still provided by their service provider. The most common here in New Zealand being Xtra, the original Telecom NZ ISP. That was fine when they were about the only ones offering internet, but now there are many more ISPs with different rates, plans, and services. There's a lot of competition, and they all offer their own email service. Why? Because it's hard to change your email address when all your friends and family know it, and so you're less likely to jump to another ISP who might be offering a great deal. It doesn't matter with your own domain name. It's independent of your ISP. You take it everywhere.
3. Online identity
Traditionally for Maori (NZ indigenous people), we were identified firstly by where we were from, and then by our family name. Our home tied us to our family, our ancestors and our tribe. It's why the first question from elders would often be "No hea koe?" "Where are you from?" , not "What's your name?". In an online world however, it's domain names that identify us. In the early days of the internet, there were only a few domain name extensions available. That's the ".com" or ".co.nz" part. .COM was for COMercial, .ORG for ORGanisations, but today you can choose from a ton of domain name extensions. You can have .business, .actor, .coach, .family. It really does allow you to customise how your online identity is first seen. First impressions count online too.
4. Provide a connection for your family