What occurs when the action of the extractor hooks over the cartridge case extraction groove?

When the extractor's hooks engage the cartridge case extraction groove, it is a critical step in the ammunition feed and extraction cycle of the M9 service pistol. This action enables the round extraction process, allowing the spent cartridge case to be pulled from the chamber after firing.

The extractor's design is specifically made to grip the rim of the cartridge case securely, ensuring that when the slide moves backward after a shot is fired, the extractor successfully pulls the case out of the chamber. This ensures that the pistol operates smoothly and prepares it for the next round to be fed into the chamber.

The other options refer to processes or functions that are not associated with the extractor's role in this context. The initiation of the firing process relates to the trigger mechanism, locking the slide pertains to the firearm's cycling and locking mechanisms, and engaging the safety mechanism involves ensuring the weapon cannot be fired accidentally, which is an entirely different function from what the extractor does. Thus, the action of the extractor is solely related to round extraction, confirming the correctness of the answer.