Alright so the Cyber Initiative is when the Grandmaster of the Lin Kuei (where Sub-Zero stays) wanted to turn his warriors into cyborgs to make them unstoppable and obedient to his control.
Some like Sektor agreed to the initiative because he thought it would make the clan better.
Others like Sub-Zero and Cyrax disagreed but were forced to become cyborgs against their will because you are not supposed to disobey the Lin Kuei once you join them.