DNS (Domain Name System)
The Internet was built on the notion that any computer on a global network can be identified by its numeric Internet Protocol (IP) address. But since people, and not machines, are the primary users of the Internet, a more people-friendly naming system called the Domain Name System (DNS) was invented.
DNS maps a host name like www.whatevercomputes.com to the IP address of the machine that hosts the Whatever computes web site. For example, DNS actually maps the host name www.whatevercomputes.com to the IP address 24.72.14.123
DNS is built upon the notion that some server's are 'authoritative' (meaning, knows all there is to know) for certain domains. A distributed name server hierarchy, beginning with the A Root Server and ending at the thousands of name servers active on the Internet, ensures that the naming and directing system works the same from anywhere.
Domain Name
A domain name is essentially a signpost on the Internet. Almost every website you've ever been to, and every email you've ever composed, has used a domain name in its address.
People register domain names in order to 'stake a claim' to a particular name -- whether for business or personal reasons.
Once a domain name is registered to a person or company, it is that person's to use exclusively as long as they continue to pay the yearly renewal fee and abide by the terms of use.
Top Level Domain (TLD)
Top Level Domain (TLD) is the portion of a traditional domain name that comes after the dot. So, in whatevercomputes.com, the top level domain is .com.
The generic top level domains (gTLDs) are .com, .net and .org.
There are also country code top level domains (ccTLDs) such as .ca, or .uk.
Second Level Domain
(SLD) is the portion of a traditional domain name that comes before the dot. So, in whatevercomputes.com, the second level domain is whatevercomputes.
Domain Name Registrar
A "Registrar" or "Domain Name Registrar" is an organization like OpenSRS or Network Solutions that has control over the granting of domains within certain TLDs (top level domains, like the generic .com/.org/.net or country-specific .ca/.us/.mx etc.).
Domain Name Registry
The 'Registry' is the system backend that is maintained by the operators of the TLD. Registrar's write new names to a central registry database, from which the authoritative root (essentially, a table of all domain names) is built. In the case of .com, .net and .org, the InterNIC runs the registry, and qualified registrars have shared access to it. In the case of many ccTLDs, the registry and registrar functions are combined within one entity.