On its own motion
Easy way to remember
Suo = his / her / its
Motu = Motion
Suo Motu (not Moto) means an act done by any person(s) in authority, with his / their own discretion and volition, without the prompting or direction of another. It means that although normally, others may cause the authority to take a certain action, usually by petition, complaint or request, the situation and circumstances were such that without such external influence, the authority took action.
The most common example is when a court takes Suo Motu cognizance of a matter and calling upon the parties to explain. The police can also take suo motu cognizance of matters which may be serious.