To quote from the BBC article:
The first decade of the net, 1972-1982, was about designing, testing and deploying the net's basic technologies.
The second decade was about consolidation and commercialisation and the third about broad, popular use.
The next decade, he believes, will see the net spread even further and start to become the basic communications infrastructure for almost anything.
To begin with, he thinks, the net will stop being a part of the telephone network. Instead the telephone network will become a part of the net.
This could be thanks to Voice Over IP technology that chops up phone calls into bits of data and sends them across the net instead of dedicated, and expensive, phone lines.