At my airport we use the Alert 1-3 system as well. Here is how we define it:
Alert 1 - Aircraft with minor difficulties. Aircraft will probably be able to land without incident or assistance.
Alert 2 - Aircraft with major difficulties. Aircraft will likely need assistance when it arrives. (Basically an accident is on its way.)
Alert 3 - Accident.
Alert 1 we gear up, get in the trucks, and just pull out of the station.
Alert 2 we stage on the taxiways adjacent the runway in use.
Alert 3 we respond to the accident.
Its all about being able to reduce response time if we have a heads up of a situation coming. FAA standards dictate we are able to respond to the midpoint of the farthest runway within 3 minutes of the initial alarm. With no advance warning, that is sometimes difficult depending on the airport layout. Alert 1 shaves about 1 minute off of the response time needed. Alert 2 puts us just seconds from the emergency aircraft once it arrives.