Hacking is a mechanism that stops the balance wheel the moment the crown is pulled out to the hour-setting position. The visible result is the seconds hand freezing in place: you wait for the reference time signal, release the crown, and the balance wheel restarts. Nothing more, nothing less.
The crucial distinction to understand clearly is this: hacking doesn't just stop the seconds hand, it stops the entire oscillation of the balance wheel. A small lever or spring blade contacts the balance wheel arbor or the balance wheel itself as soon as the crown exits the first detent. When you push the crown back in, the lever retracts and the balance wheel resumes from the exact angle where it was locked. Synchronization to the second is real, not approximate.
Historically, this function originated in military and aeronautical contexts. Pilot watches—German Flieger watches foremost—adopted it early because dead reckoning navigation requires a verified start time to the second. Not coincidentally, the COSC chronometer movement standard includes it, and many certificates from the Bienne office list it as a requirement.
Regarding production-grade calibers, the comparison between the old Seiko 7S36 and its successor 4R36 is instructive: the 7S36 has neither hacking nor manual winding, while the 4R36 adds both. It's a step up in category that you feel in daily practice. Similarly, the base Miyota 8215 lacks hacking, while the 9015 has it: anyone buying knows what they're choosing.
There is a variant worth mentioning separately: the Grossmann mechanism on caliber 100.1. Pulling the crown stops the movement, but it remains in position thanks to an internal spring. Restarting requires a separate pusher under the case. It's a solution that also reduces dust ingress. Functionally it is hacking, but with deliberately different ergonomics from the rest of the market.
A point of clarification: one source in my notes associates hacking with the chronograph function in the El Primero 3620 SK caliber. This is a confusion. In a chronograph, a hacking mechanism may exist on the central seconds hand of the chronograph itself—it is not the same function as hacking on the main time. These are distinct devices that share a name but serve different purposes.