Domain name registration is the act of reserving a name on the Internet for a certain period, usually one year.
It is important to know that this domain will remain yours for as long as you renew it and there is no way to purchase a domain name forever.
Domain name registration is necessary for a website, an email or another web service.
However you don't have to always register a new domain name.
Many companies allow you to use subdomains of their domain names for a website, or you can have an email with their primary domain (ex. yahoo.com, gmail.com).
The most important thing about a domain name registration is that it gives you personality and recognized identity.
Once you register a domain name, the information about its owner is publicly available.
The price for a domain name registration varies greatly on its extension.
For example, the most common .com is the most affordable one, while some country-specific domain name extensions are 5 times more expensive.
You can check the availability of the domain here.