For the same reason GPS satellites have atomic clocks.

In the case of old ships, it was all about navigating very precisely by comparing moving visual reference points (i.e., stars), against a reference that then derives the location based on one's position relative to those reference points at a given time.

Any increase in error in either of the two inputs will cause significant positioning errors. The quality of the sextant and the navigator determined the error of the visual reckoning of one's position relative to the stars, the time error was down to the quality of the on-ship chronometer. A trustworthy deck chronometer used to be one of the most important pieces of tech on the planet. Zeroing that chronometer to a trustworthy timekeeping reference while in port is the idea here.

If the earth neither orbited nor turned, the time component wouldn't be necessary. (That isn't entirely true: nothing in space-time between the navigator and the stars would be able to move without introducing an error rate, but the error rates would probably be low enough for that not to be a factor. If I were less lazy and more educated I'd try to work out how much error that introduces.)

Everyone should buy an inexpensive training sextant (e.g., Davis Instruments Mark III Training Sextant) and learn the basics of how celestial navigation works. (For the inclined, there are also good training videos on YouTube.)

It was used by Chronometers on ships as a sync event. Earlier they had put up a time ball on Canton Hill but that could not be seen by sailors due to fog.

Note: The gun is fired at 1pm because they have to fire it just once thus saving cost. Other ideas were considered such as firing it 9 times at 9pm.

So they would know exactly when to fire their local time guns

I am not sure I understand. If there were local time guns, wouldn't they just fire theirs when they heard the sound of the central gun to help sync time with those farther away? They couldn't fire their gun 10 seconds in the past when they heard the central gun's sound.

Hmm, either option would actually lead to mass confusion; various intermediate locations wouldn’t know which cannon was which.

Just wagering a guess, but presumably to synch their clocks to a known good time?

A commenter to the wikipedia page I posted about the vancouver 9 o'clock gun makes a compelling point: it was all about providing a time signal for ships in port to set their onboard clocks.

That makes sense. Ships used time to help get their location back then and presumably even a second deviation could put you off course.

Ships also used Greenwich Mean Time (which this cannon is tied to) and astrological data for local time (which this cannon also used for its time).

But why down to the second? I can see why syncing clocks +/- 30 seconds could be useful (train schedules, etc.) but this chart is about being within a second.

-Surely if you are going through the trouble of setting your clock, you might as well do it accurately?

Also, as suggested by others (I should have thought of that!) - ships used chronometers to establish their longitude.

(At 56 degrees north, which Edinburgh lies on, a timing error of a second translates into 18 meters or so - an order or two of magnitude below the accuracy of even the best of celestial navigators - but still, might as well make the starting conditions as good as possible.)

NTP nerds before NTP