The Internet grew out of a research program sponsored by the US Department of Defense Advanced Research Projects Agency. D/ARPA was created in 1958, the depths of the Cold War, to oversee and coordinate military research projects. It was established shortly after the Soviet Union had shocked the United States by successfully launching the Sputnik satellites, threatening American pre-eminence in science. Sputnik prompted the Eisenhower administration to place a new emphasis on science and mathematics education and government-funded scientific research. D/ARPA has funded a large share of the computer science research in industry and academia over the four decades of its existence.
The original motivation for the program that gave rise to the Internet was to strengthen the technology for Command and Control of military systems, and particularly the US nuclear weapons systems. Many of the participants in the project had previously been involved with SAGE, a massive Cold War engineering project that built the first distributed system for real-time interactive control. The SAGE project first established the radical idea of the computer as an interactive medium with a visual interface and a pointing device, rather than merely a tool to speed calculations.
From the start, the D/ARPA program used the Command and Control motivation to frame a much larger research agenda that would change the way that people saw and used computers, not just in the military but in civilian and business sectors as well. The visionary in charge of this program was JCR Licklider. Licklider was a psychologist by training, and he had helped to establish psychology as a scientific discipline focusing on human thought processes. This view eventually supplanted the behaviorist approach of BF Skinner, which considered stimulus/response behaviors as the only legitimate focus of objective study, and denied that internal mental states and processes could be studied scientifically or even that they existed.
One of Licklider's central interests throughout his life was the use of machines to augment and enhance human capabilities and human experience. The invention of the digital computer offered exciting new opportunities to realize his vision, and his appointment as a D/ARPA program director offered the means. Licklider's program sponsored groundbreaking research at MIT, Stanford, Berkeley, RAND, and elsewhere that laid much of the foundation for computing systems today.
Licklider's vision of a computer network to enable human communication and collaboration was viewed by leaders in the computer industry and academia as preposterous at the time. Computers were large, expensive beasts, and it was difficult to envision how sufficient computing power could be harnessed to support this vision, or even how it might be used. Few could imagine graphical user interfaces and the World-Wide Web, or the degree to which such a facility would be integrated into daily life a mere four decades later.
Licklider did not like to write, but he did set out the elements of his vision in two informal but seminal papers: Man-Computer Symbiosis (1960) and The Computer as a Communications Device (1968, co-authored with Robert Taylor). These papers can be found on The Matrix: JCR Licklider. Please read them in sufficient detail to get the feel of his radical ideas and the perspective of the time. Licklider's vision is also summarized and discussed in The Vision of Interactive Computing and the Future and elsewhere on the Web.
Also, please read Chapter 1 of Where Wizards Stay Up Late for this discussion.