What does the accuracy of a watch mean?

Accuracy of a mechanical watch
A mechanical watch operates using the power that is generated when the mainspring, which has been wound manually or automatically, is unwound. The time accuracy mainly depends on the performance of "balance" which oscillates mechanically.
Oscillation frequency of the balance varies from a typical beat of 5 to 6 beats/second to a high beat of 8 to 10 beats/second. The accuracy increases as the beat number becomes higher. Time accuracy varies from several seconds/day to several tens of seconds/day.
With respect to durability, it is difficult to increase accuracy by raising the oscillation frequency; however, some highly accurate mechanical watches (loss/gain: at a level of ±5 seconds/day) are equipped with a hand-brake adjustment device which mechanically makes slight accuracy adjustments of the watch.
The accuracy of a mechanical watch may be affected by the amount that the mainspring is wound, position of the watch, temperature, shock from outside, magnetism, etc.
Therefore, the accuracy of a mechanical watch indicated in watch catalogues is measured when the amount that the mainspring is wound, position of the watch, and temperature are under certain conditions. Furthermore, when the watch is worn on the wrist, the accuracy of the watch may be out of the accuracy range indicated in watch catalogues. That is why information on accuracy is not indicated in some mechanical watch catalogues.
Accuracy of a quartz watch
The greatest virtue of a quartz watch is its high level of time accuracy. Time-keeping of a quartz watch is based on the crystal oscillator of high frequency (32,768 Hz). As for a mechanical watch, the minimum accuracy is ±several seconds/day; however, the accuracy of a general quartz watch is ±20 seconds/month.
For achieving higher time accuracy, high precision quartz watches are being made by making the crystal oscillators of a higher frequency, introducing various temperature adjustment functions, or using automatic time adjustments through radio wave reception which contains official standard time information.
The crystal oscillator is a tuning fork-type oscillator and is affected by temperature. However, compared to the balance which oscillates mechanically using a hairspring, the crystal oscillator is not easily affected by shocks or position of the watch, and is more reliable against outside elements which may affect time accuracy. As a result, you can use a quartz watch for a long time without worrying about loss or gain. Please note that the analogue quartz and combination quartz watches with built-in step motors are affected by magnetism.
Because the quartz watch obtains energy from a battery with stable voltage, its functions including accurate time keeping operate stably for a long time. Using electronic parts, the quartz watch has a low failure rate compared to a mechanical watch; and as a result, it has high reliability.

(Note): The above information applies to the members of
the Japan Clock & Watch Association and their products.