The United States Defense Department created the Internet in the 1960's under the name ARPAnet (Advanced Research Projects Agency Network) as an experimental network. The ARPAnet connected computers across the United States, regardless of operating system or hardware, to ARPA research sites. But costs were high.
In the meantime, the National Science Foundation built its own high-speed network, the National Science Foundation Network (NSFNET), that connected supercomputer sites to it. The NSFNET made the ARPAnet obsolete.
In 1994, Tim Berners-Lee and Robert Cailliau at CERN, a physics research center in Switzerland, developed the Web. Note that the Web is not the Internet; the Web runs on the Internet.
In 1995, the National Science Foundation closed the NSFNET, passing all the Internet traffic to corporate networks such as MCI. This marked the beginning of the Internet.