The Internet started life as a report written by the Rand Corporation for the US government in the 60s. This outlined very much the modern view of Information supplanting material goods as the commodity of the coming century.
The US government agency ARPA, the Advanced Research Project Agency, invested several billion dollars in developing "Packet Switching Networks" through the early 70s. Initially, the customer for these was the US Department of Defense. However, many of the researchers contracted to carry out the work were academics. They became enamoured of the test systems they built, initially the research network was called the ARPANET, and later the Internet.
By the very early 80s, two other important pieces of technology had emerged. Firstly the workstation/server system was starting to emerge as the way to provide cost effective computing to the desktop. Secondly, the Ethernet Local Area Network was accepted broadly as the way of providing communications between the desktop and server computers in the same organisation.
The same researchers used all these systems for computing, local, and national (US) communications.
A curious footnote to this history was that the US government funded most of the initial implementations of the Internet technology on the basis that it would be made freely available to others.
This was in direct contrast to the expensive communications solutions provided by computing and telecommunications companies that conformed with International Standards promulgated by the ITU (International Telecommunications Union) and ISO (International Standards Organisation).
By the late eighties, a large proportion of universities and research labs in Europe and the US had access to the Internet through largely government subsidised network links leased from the Public Network Operators. However this changed rapidly, so that now many Internet connections are paid for directly by the subscribing organisation.
On the standards front, it became obvious that people were 'voting with their feet", but that the Internet Protocols (the communications languages used to glue all this together) needed to have a more acceptable status. Hence, the Internet Society, an International not-for-profit professional body formed to allow individuals, government agencies and companies to have a direct say in the direction that the protocols and the technology could move.
This is now very much the state we are in today, and except for one other thing, would not really explain the very recent massive growth in interest in the Internet. That one thing is the World Wide Web, of which more in a moment.