Domain names are part of the domain name system - which is a system that uses words/charcters to access an IP address. Every resource (computer) on the Internet is assigned an IP address, and domain names make it simple for the end-user to access an IP address. Domain names also help to create a unique identity for online services, which can change IP address (physical address) but can be accessed easily with the same domain name.
The domain name system has a hierarchy: the top is the root domain (controlled by IANA) and below that is top level domains that are maintained by a registry (assigned by IANA). Some examples of top level domains are: org, com, net, and uk. It is possible for end-users to register a namespace within these top level domains; a namespace being a name. However, the end-user cannot (usually) register a namespace with the registry. Instead, accredited registrar's (like tucows) pay the registry on behalf of the end-user and manage the domain name (namespace) for them.
The end-user is named a registrant. The registrant is viewed as the "owner" of the domain name, but, the registrant requires a registrar to manage the domain for them. When a registrant registers a domain name, they have to supply the following information: name, address, telephone number and email address. A registrant will also have to supply a registrant "type"; for uk domain names, the following registrant types to choose from are:
For some top level domains - most uk domain names - if a registrant is a non-trading individual: they can then opt to have their address omitted from the whois service. The whois service allows users to verify who has registered a domain name.
Registrants can transfer management of their domain name to another registrar. Why would a registrant want to do transfer management? some registrar's charge less to renew a domain name, and registrar's vary in the amount of management options they provide for a domain name. Ideally a registrant should have full DNS control. Registrars can charge a fee to registrants to transfer management of their domain.