Cerebro is a divice for telepaths who Professor X uses expanding his telepathic ability to look at all the mutants and humans around the world. Cerebro can kill everyone in the world leaving Xavier behind but he would never do that. Cerebro is at the X-Mansion in the Subasement and is one of the most reliable divises. There is only one but there have been other designs.
Other Designs
Beast made the first ever Cerebro and made Professor X use it. This is how they started the team by finding other mutants to recruit to their team.
William Stryker made a Dark Cerebro to kill all mutants brainwashing Professor X. That Cerebro was destroyed.
Cerebro on the Marvel Wiki