One-alarm, two-alarm, three-alarm fires, are categories of fires indicating the level of response by local authorities, with an elevated number of alarms indicating an increased number of phone alarms went off during the fire. The term multiple-alarm is a quick way of indicating that a fire is severe and is difficult to contain. This system of classification is common in the USA and in Canada among both fire departments and news agencies.
A common misconception is that a "3-alarm fire," for example, means that three firehouses responded to the fire. This is not the rule behind the naming convention, although some cities may use the number of firehouses responding for multi-alarm designations because that is the simplest way to determine an alarm number.
The most widely used formula for multi-alarm designation is based on the number of units (firetrucks for example) and firefighters responding to a fire; the more vehicles and firefighters responding, the higher the alarm designation. (Note: In most cities, a "unit" can be anything from a tanker or ladder truck to rescue vehicles to even cars driven by the chief and deputies.)
With this unit/firefighter alarm designation, the initial dispatch is referred to as a "first alarm" and is typically the largest. Subsequent alarms are calls for additional units, usually because the fire has grown and additional resources are needed to combat it, or that the incident is persisting long enough that firefighters on scene need to be replaced due to exhaustion.
Requests for units and firefighters from outside jurisdictions do not normally occur in multi-firehouse urban areas until elevated alarms are reached (alarm three and above), but will depend on the location of the incident and the condition of the authority having jurisdiction at the time of the incident.
The system of classification comes from the old tradition of using pull stations to alert the local departments to a fire in their area. The "box" would send a message to all local stations by telegraph that there was a fire, indicating the location as a number: (station area)-(box number), e.g., 2-11. Fires are still dispatched as "box alarms," following this tradition, with maps broken up into a grid of "box areas."