Paul-
The number of an alarm has to do with the number of trucks sent. Depending on where you live, a 1st alarm will get you 2 pumpers, 1 ladder truck, an ambulance and a duty officer(Battalion Chief). Each following alarm is more of the same. Obviously, the bigger the fire, the more alarms needed. Sometimes extra alarms are called for if the weather is extrememly hot or cold to help keep firefighters fresh.
Hope this helps you.
Have a good day.

MJA

firewoman