The Cyber network was the network that linked every Cyberman to one another. It contained their database and was used transfer files wirelessly. (TV: Rise of the Cybermen) It could also receive information from infostamps, giving Cybermen a means of exchanging information when their wireless systems were inactive. (TV: The Next Doctor)
To defeat the reviving ship of Cybermen that crashed in Klimtenburg, the Eleventh Doctor cut off a partially-converted Victor Ernhardt from the Cyber-network. Victor's Cyber body was then charged with excess power from a lightning stike so when he was reconnected to the network, the other Cybermen overloaded and died. (PROSE: Plague of the Cybermen)
Marcus Bertrand, assimilated into the Borg Collective, set all Cyber Ships present in the Federation universe to self-destruct over the Cyber-web after the defeat of the Cyber-Controller. (COMIC: Assimilation²)