Mechanics
The stardust watch allows the player to go 1 hour into the future at the cost of 100,000 Stardust
.
NOTE: This fast forward of time does not effect timers or things that are server related. This means things like the distance to the moon and sun, or the timer of the monster holding the purple key, will not change when using the watch.
However, actions such as finding gems, gathering, and fishing are calculated as if 1 real hour had past.
Charges
The watch has a limit on how often it can be used in the form of charges. The max number of charges on the default watch is 20.
Charges for the watch are randomly obtained over time with an average of 1 charge every 24 hours.
Red Stardust Watch Orb 
The max number of charges is increased to 40.
The rate at which charges are received is doubled.