A domain name is an identification string that defines a realm of administrative autonomy, authority or control within the Internet. Domain names are formed by the rules and procedures of the Domain Name System (DNS). Any name registered in the DNS is a domain name. Domain names are used in various networking contexts and for application-specific naming and addressing purposes. In general, a domain name represents an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, a server computer hosting a web site, or the web site itself or any other service communicated via the Internet. In 2017, 330.6 million domain names had been registered.
Namecheap is a solid choice for registering your domain name. Plus, their site is incredibly intuitive and easy to use, especially on their domain management pages, which can be incredibly helpful. They offer reasonable priced domains, and have a free DNS service, and WHOIS protection. They also offer SSL encryption, for those looking to beef up the security of their domains.
Note that you can also transfer your domain name from one registration service to another. You'll want to do this if you're not satisfied with your current domain hosting service, if you find a better deal when your current registration is coming due, or, most likely, if you've signed up with a web hosting service that will also transfer your name to its site. Expect to get the transfer for free, but if that isn't offered, search for another domain hosting service.
If you're having trouble finding a domain name (whether because of crowding or cyber-squatters), check for a help facility on each registrar's site. Domain registrars typically house search engines that return a listing of available names similar to the one you want. When you search for a domain name at Namecheap, for example, you get both the status of that name and a list of suffixes available for that name. Maybe [Sitename].com isn't available, but [Sitename].biz or .org is.
GoDaddy used to be a place I'd recommend only as a joke, but has significantly improved their service. They'll recommend you domains based on certain keywords, which is useful if you've not got the one you want available (they'll actually remove these from the search to try and not break your heart), and they've also significantly improved their hosting offering. They still continue to offer weird things like "email services" that other hosting companies provide too. Our GoDaddy Review.
The practice of using a simple memorable abstraction of a host's numerical address on a computer network dates back to the ARPANET era, before the advent of today's commercial Internet. In the early network, each computer on the network retrieved the hosts file (host.txt) from a computer at SRI (now SRI International), which mapped computer host names to numerical addresses. The rapid growth of the network made it impossible to maintain a centrally organized hostname registry and in 1983 the Domain Name System was introduced on the ARPANET and published by the Internet Engineering Task Force as RFC 882 and RFC 883.
In order to register any domain, you must provide certain personal information that you may not wish to be publically searchable in the Whois database. Signing up for WhoisGuard is a great way to keep your registration data private. WhoisGuard acts as a "shield" for your searchable information, displaying the address, phone number, and email of the domain registrar (Namecheap, e.g.) instead of your own. Keep in mind that WhoisGuard is an optional security add-on that must be renewed separately when you renew your domain.