Why it matters
Continuity is the reason. If scene 14 at Rosie's Diner was shot with the ketchup bottle on the left of the counter and a coffee cup half full, and scene 19 at the same counter shoots two days later, those items have to be exactly where they were. The on-set set dresser and props take photos, but it's much faster if nobody moved them.
The same applies to lights on a stage. If electric leaves a rig in place overnight for tomorrow's continuation of the scene, the set is hot, and a cleaning crew or another unit shouldn't touch it.
On the schedule
The stripboard determines how long a set stays hot. Say the diner is day 3 and day 5, and day 4 is at another location. The diner stays hot through day 4, so the production pays to hold it (location fee or stage rental), and security may be needed overnight.
A fictional note on day 3's call sheet:
Rosie's Diner remains HOT SET through Day 5. Do not strike counter dressing. Location closed to public Tue to Thu per agreement.
Day 4 might also be the diner's cover set day in case of rain, which is another reason to keep it hot.
Releasing a set
When the last shot at a set is approved, the 1st AD confirms with the script supervisor and director that nothing else is needed there, then announces the set is wrapped. The set decorator's team can then strike. On a rented location, that release starts the clock on returning the place to its original condition.
Mistakes
Striking too early is the classic mistake. A set gets released at the end of day 5, the art department clears it that night, and the next morning the director asks for a pickup shot of the counter. Re-dressing from photos takes hours. ADs should hold a set until dailies from the last day there have been checked, when the schedule allows.
Unmarked hot sets cause trouble in shared spaces. On a stage with more than one set, or at a practical location where the owner's staff still work, put up signs, tape off areas, and tell the location contact what they can and can't touch. The set decorator usually owns the signage.