The Worldwide Network is a vast information database in the world of Final Fantasy VII roughly equivalent to the real world Internet. Unlike the Internet, the Worldwide Network is highly interactive, to the point that whole personas can be uploaded onto it.
In spite of the Worldwide Network's usefulness it appears to be used mainly by Shinra and does not seem to be freely accessible to the general public. This may be because the network is owned and operated by Shinra, who would likely not want the public to have access to a network where information is much more difficult to regulate and suppress (the suppression of information being one of Shinra's top priorities). Although it would seem that Shinra does use the Worldwide Network for some civilian applications, like sending and receiving electronic messages via communications devices like cellphones.
The Worldwide Network plays a minor role in Crisis Core. Zack Fair can receive E-mails from various people during his adventures. He can also use the stores from around the Planet and receive and take missions at save points.
The Worldwide Network plays a much larger role in the plot of Dirge of Cerberus. Professor Hojo, working at the computer of the Sister Ray Cannon, managed to upload his mind onto the Network just before AVALANCHE comes to kill him. The fall of Meteor badly disrupts and fragments the Network, doing the same to Hojo. His shattered pieces wait inside the off-line Network until the World Regenesis Organization puts it back online.
When Weiss takes a Synaptic Net Dive, Hojo begins to possess his mind. Slowly, Hojo takes control of him until Weiss is just a puppet. From there, Hojo takes command of Deepground, and begins his next experiment.
Shelke is ordered to find the work of Lucrecia Crescent on the power of the Omega Weapon and Chaos. During Shelke's recovery of the data, she gains some aspects of Lucrecia's personality, and slowly begins to recover her emotions. It also causes her to develop feelings for Vincent Valentine.
Hojo is eventually purged from Weiss, and is presumed to have been completely destroyed.