As you may know, the Internet was originally designed as a "command and control" network for the US Military in the 1960s. The funders and architects desired a nework, independent of the phone system, which would allow for communication between different key military research sites. The network allowed scientists to log in to mainframe computers from remote locations. It was a cool enough idea. The network planners then did a neat thing: they allowed graduate students at the Universities which housed these research labs to use the network.
These original users had accounts on the mainframes, and logged in to run programs. But people soon discovered other uses for the network beyond the intent of the designers. People began to send e-mail as often as they ran programs on the mainframes. People found new and personal ways of using the technology.
A neat thing about the way the Internet was set up was that it was an open system, the specifications of which were published publicly. Anyone so inclined could figure out the details of the TCP/IP protocol on which the network was built. The standards and protocols were accessible to everyone who could understand them. So when people thought of a new use for the network that hadn't been implemented, they could just write some new programs which could operate on the network. What followed was a torrent of new uses for the network. People wrote programs to login to other computers (telnet, rlogin, rsh, etc.), to transfer files (ftp, tftp, uucp, etc.), to check to see if another user is online (finger), to chat with other people (IRC, talk, etc.), and the list goes on and on.
The web is an example of such a program.
Another interesting thing to consider about the Net is that it has been shaped by the free exchange of information and ideas. When someone wrote a new program which added new functionality to the Net, they often made the code freely available to other users. There is no central administration of the Internet, and the system administrators of each local network connected to the whole can decide what programs to run on their systems. This has nurtured an atmosphere of experimentation and sharing which is very different from conventional business practices. The wide variety of computers connected to the Internet has prompted people voluntarily accept standards for particular types of programs to ensure the inter-operability of different operating systems and hardware. Thus, even as programmers develop new innovations, they often publish the specifications of their work, ask for public comments (an RFC), and a lot of debate happens before an new way of doing something is widely accepted as a standard.