A directed network (or graph) is a network in which each edge has a direction pointing from one vertex to another vertex.
In case of WWW , when we go from one page to another (to be more specific, say in same tab), we can always go back to previous page from the new page, which shouldn't be possible as in directed networks if two vertex are joined by unidirectional edge then there is only single path in between those vertices.
In a directed graph, the direction plus a "don't go backward" rule would imply there is only one way to traverse a link. The "don't go backward" rule is optional.
On the other hand, the "back" button of your browser does not actually use the link you just followed to go "back," but instead uses its own stored history of your browsing to find the previous page viewed.
It seems someone was trying to motivate directed graphs with some "real world" examples, and they chose an example that does have a directed graph at least partly involved, but the actual WWW and the way we interact with it is so much more complicated that the example may not really be very helpful. I suggest just moving on to the actual topic.