The Z-Bomb was a doomsday weapon which, if activated, would explode with a force strong enough to split an Earth-sized planet in half.
By December 1986, two or three were placed at strategic positions around the Earth. One of them was in the hands of the International Space Command and their secretary general had the authority to order it used. To prevent the unauthorised use of a Z-Bomb, the station holding the bomb must gain clearance from Geneva. This particular Z-bomb was located at Snowcap base in Antarctica.
When Cybermen ships were heading for Earth, General Cutler wanted to use the bomb to destroy Mondas, despite concerns voiced by the First Doctor that the radiation would kill everyone on the side of the Earth facing it and Mondas might turn into a supernova. Cutler considered this an acceptable risk, but his personnel sabotaged the missile. The Doctor's companion Ben Jackson assisted them.
When the Cybermen took control of the base, they planned to use the bomb to blow up the Earth, saving their own planet from the effects of the energy transfer between the two worlds. They failed and Mondas was destroyed. (TV: The Tenth Planet)