Want to know how the manipulator with the ROV works and how it opens and closes
If you’re talking about the Newton Subsea Gripper the video on the page explains how it works, and the Technical Details and Learn sections at the bottom describe the extent of motion and the required PWM signal to open/close the gripper.
As it says in the Product Description section,
The jaws are driven by a linear actuator that uses a geared brushed motor and lead screw.
The same section also specifies that
The motor is controlled by a purpose-built brushed motor controller that accepts a standard servo-style PWM signal so that the gripper can be controlled just like our thrusters and lights.
So basically they use custom electronics to take in a PWM signal and actuate a brushed DC motor, which turns some gears (likely to improve the efficiency and increase the output torque), which turn a lead-screw, and the gripper jaws are pushed open/pulled closed by the linear motion of a carriage on the lead-screw.
Something like this: