n. 1. The union of all the major noncommercial, academic, and hacker-oriented networks, such as Internet, the old ARPANET, NSFnet, BITNET, and the virtual UUCP and USENET 'networks', plus the corporate in-house networks and commercial time-sharing services (such as CompuServe) that gateway to them. A site is generally considered 'on the network' if it can be reached through some combination of Internet-style (@-sign) and UUCP (bang-path) addresses.
2. A fictional conspiracy of libertarian hacker-subversives and anti-authoritarian monkeywrenchers described in Robert Anton Wilson's novel 'Schrodinger's Cat', to which many hackers have subsequently decided they belong (this is an example of ha ha only serious).
In sense 1, 'network' is often abbreviated to 'net'.
"Are you on the net?" is a frequent question when hackers first meet face to face, and "See you on the net!" is a frequent goodbye.