Final answer:
The lanyard attached to a PWC's start/stop switch is important because it shuts off the engine when the rider falls off, preventing the PWC from operating without a driver and reducing the risk of accidents.
Step-by-step explanation:
It is important to have the lanyard that connects to the Personal Watercraft's (PWC's) start/stop switch attached to your wrist or Personal Flotation Device (PFD) because it shuts off the engine in case you fall off. This safety feature, often referred to as an engine cut-off lanyard, is crucial for preventing the PWC from continuing to operate without a driver, which can be dangerous for both the rider who has fallen into the water and other people nearby. It helps to prevent accidents and potential injuries that could occur if the PWC runs away or hits someone or something.