Well, more than just a website, I'd call it a domain name to be used for various personal services, starting with email. A domain name is like your home address in the physical world; not having one is like not being a citizen of civil society.

As for the domain, well, one can also have a website to introduce yourself to the world, the usefulness is marginal for the average person, but yeah, you can have one. It can be used as a sort of business card, an interactive CV, or your own little corner to tell the world what you think; it has many uses and each has implications to consider. But the domain is the essential part. It's about having your own mail even if you use GMail (for domains), so that one day you can switch providers without changing anything for your contacts. It's perhaps hosting XMPP or Matrix for yourself to talk to friends, family, and sometimes even total strangers without depending much on other people's services. It's about serving your own web apps to yourself on the go. The website itself matters less in all of this.