Short answer: Florida law lets carriers apply a separate, higher hurricane deductible, calculated as a percentage of your dwelling coverage, that kicks in when a named hurricane causes the loss. It applies from the time a hurricane watch or warning is issued until 72 hours after it ends, and typically once per calendar year, not per event.
The math
On a $400,000 dwelling with a 5% hurricane deductible, you pay $20,000 before the carrier pays anything for hurricane damage.
When it applies
The hurricane deductible applies from the time a hurricane watch or warning is issued by the National Hurricane Center until 72 hours after it ends.
Once per season
Most Florida policies apply the hurricane deductible once per calendar year, not per event. If multiple named storms hit, the first satisfies the deductible.
How to reduce it
At renewal, you can typically choose a lower hurricane deductible for a higher premium. Do the math.