A domain name registration is simply reserving your website's name for a specified period of time. The two parties involved with a domain registration are generally the user who is registering the domain and the domain registrar. The domain registrant is the user who actually registers the domain name and the domain registrar is the company who helps that user with their domain registration.
The way that competition is supposed to work between registries, is that lots of companies go to ICANN and say “We think we can reliably manage .com, and we think it would cost us [$5] per domain.” ICANN reviews these bids and awards the .com contract, which lasts for a fixed period of time, to whomever they deem best-suited to the job. In this time, other companies can think of ways to manage .com better/cheaper, and try and win the next contract. This, in theory, would provide an incentive for registries to innovate, a big part of which would be in lowering costs.
Who is in charge of all of these processes? Most countries manage a Network Information Center (NIC). An NIC is the main database that has all the information regarding what domain names have been registered and the IP address associated with each of those domains. The nonprofit organization the Internet Corporation for Assigned Names and Numbers (ICANN) is in charge of creating and managing the procedures for internet namespaces.
Premium domains (also known as aftermarket or pre-registered domains) are short domains, often just one word or even just 3-5 letters. Most of them have a .com extension but many premium domains end with .org, .net, and .biz. These domains include common words and are generally the most memorable. Because companies value short domains that match their company name or products, these domains are typically the most desirable. Additionally, certain domains sold by different registries are considered premium and therefore have a higher price point. In some cases, the renewal costs of these higher-priced domains are also quite expensive. Some high-priced premium domains, though, renew at a regular (lower cost) rate, giving you a better value in the long term. Make sure to research the overall cost of the domain plus renewal to find the right domain for your budget. You can browse Namecheap's premium domains in our Marketplace.