A registry is a database integrated into certain operating systems which store information, including user preferences, settings and license information, about hardware and software installed on a user's computer.
Domain Name System
A registry (domain name registry) is an entity that operates and administers the master database of all domain names registered in a top level domain. Generally, ccTLDs are run by designated registries in the respective countries, and gTLDs are run by global registries.
For example, VeriSign, Inc. currently manages the name servers for the .com and .net TLDs, a nonprofit entity called Public Internet Registry (PIR) manages the name servers for the .org TLD, another nonprofit organization called EDUCAUSE manages the name servers for the .edu TLD, and Neustar, Inc. operates .biz).
All of these registry organizations are subject to change, however. A list of current agreements between ICANN and registry operators is available here.