Very Simple: A hacking watch is one which allows you to stop the second hand.
Why is this important or useful?
For one thing, it allows you to align all three hands on a specific time. Let’s say 1:03:00. Then, you wait for your known good time keeping source to hit that same time, 1:03:00. When it does, you release your watch hands to move again. This way, your hour, minute, and second hands are all right on time!
If you cannot stop your second hand, only your hour hand and minute hand will be set. The second hand could be at any point on the dial, so your watch will be “off” by up to 30 seconds either fast or slow.
Note that hacking a watch has nothing to do with the accuracy of your watch going forward, only the accuracy of the time at which your watch is set.
All of this is only possible in a mechanical watch which needs to be manually wound.
There is another important capability that is unlocked if a group of people have hacking watches: They can synchronize their watches!
Have you ever wondered how military personnel could all launch attacks at the exact same time or maneuver at the same time? It was because they had hacking watches and they set their watches together. Therefore, all of their watches showed the exact same time, down to the second.
What is a hacking watch? A watch that has a second hand that can be stopped.
What is mechanical watch hacking? Using the hacking feature to set your watch to the exact precise time, or for a group of individuals to synchronize their watches.