There has been a long historical debate on when the Internet first came about. The first thing you have to do to keep it very straight is to define the terms and whether the debate is talking about the first network, the "World Wide Web" or the larger Internet. Since so many people at all levels of expertise use these terms interchangeably --and their organic terms anyhow-- it can get difficult and confusing.
However, there was a moment on a usenet message board system where an expert in these matters named Tim Berners-Lee first outlined and proposed the WorldWideWeb as a project. Thanks largely to the fact that these mailing lists have been archived in many places, including Google Groups, we can go back and see the message as it was first posted, typos and all.
The WWW project merges the techniques of information retrieval and hypertext to make an easy but powerful global information system.
The project started with the philosophy that much academic information should be freely available to anyone. It aims to allow information sharing within internationally dispersed teams, and the dissemination of information by support groups.
Read the full message on WorldWideWeb Summary.