The Internet is real, and so is its physical infrastructure. Its infrastructure consists of millions of miles of fiber-optic and copper cable as well as hardware that is needed to transmit data over these cables and wirelessly.
The Internet is not operated by a single company or government but is really a network of interconnected networks. As of early 2018, the Internet consists of some ~60,000 interconnected networks. The Internet and its topology and infrastructure has reached enormous complexity and keeps many researchers around the globe busy trying to map it with at least some degree of accuracy.
Data servers all around the world!