IANA stands for Internet Assigned Numbers Authority, the term was coined by Jon Postel and Joyce Reynolds. Postel was part of a team of computer scientists who created the first node (location) of ARPANET at UCLA (University of California at Los Angeles). IANA was an unofficial/informal agency that was created to manage and develop the technical architecture of ARPANET.
IANA operated on an informal basis during the 1970's and 1980's: during this era IANA did not have a specific name, but there was always a group of individuals - usually headed by Jon Postel - that assigned numbers for Internet protocol related services. It was during 1990, as the Internet began to evolve from it's academic ARPANET roots, that IANA was formally named and organised.
In March, 1990, Jon Postel and Joyce Reynolds released a Request for Comment document (1060) titled "Assigned Numbers" that first made mention of IANA. The document stated: "This RFC will be updated periodically, and in any case current information can be obtained from the Internet Assigned Numbers Authority (IANA). If you are developing a protocol or application that will require the use of a link, socket, port, protocol, etc., please contact the IANA to receive a number assignment."
IANA's role has expanded beyond assigning numbers for Internet protocol related services: it also administers the root zone of the Domain Name System(DNS); the DNS was created in 1984. IANA also assigns IP address blocks to global regions and assigns port and socket numbers to Internet services (protocols) like the World Wide Web (HTTP application layer protocol).
IANA had been the exclusive 'domain' of the computer scientists who developed ARPANET in the early 1970's; however, they were funded and under contract to the United States Department of Defense. IANA would eventually come under more stringent oversight by the United States Department of Commerce in 1998. This was as a result of Jon Postel controversially, and on his own authority, "hijacking" the Internet by instructing eight regional root nameservers to change the root zone server they "pulled" addresses from.
The United States Department of Commerce, in response, released a document called "A proposal to improve technical management of Internet names and addresses" which resulted in the creation of ICANN. IANA would become a department of ICANN in 1998, and IANA would henceforth be overseen and adhere to United States Department of Commerce policies. From 1998-2014 (present day) IANA has been a department of ICANN; ICANN is a corporate business, located in America, that is run on a nonprofit basis under contract to the United States Department of Commerce. There are plans to decouple IANA from ICANN and move management to a global stake-holder community.
On the 1st of October, 2016, ICANN and therefore IANA, was freed from U.S. government oversight, and has now transitioned to multi-stakeholder governance.