Skynet is the computer system that becomes self-aware in The Terminator.
In the franchise’s central backstory, Skynet is an artificial intelligence created for military defense. Once it becomes self-aware, human operators attempt to shut it down. Skynet interprets the action as an attack and launches nuclear weapons, beginning the catastrophe known as Judgment Day.
Skynet then wages war against the surviving human population by using automated weapons, factories, and Terminators. Its decision to send a Terminator into the past creates the time-travel conflict that drives the original film. Kyle Reese travels back to protect Sarah Connor, while the machine is sent to kill her.
Cyberdyne Systems is the company associated with developing the technology that leads to Skynet, but Cyberdyne is not the computer system itself. Genisys is a later name for a related artificial-intelligence platform in Terminator Genisys, and “the Turk” refers to an earlier fictional system in the wider mythology.