An airbag is designed to inflate in moderate to severe frontal or near-frontal crashes. The airbag will inflate only if the impact speed is above the system's designed "threshold level." If your vehicle goes straight into a wall that does not move or deform, the threshold level for the reduced deployment is about 10 to 15 mph (16 to 24 km/h)
The threshold level can vary, however, with specific vehicle design, so that it can be somewhat above or below this range. If your vehicle strikes something that will move or deform, such as a parked car, the threshold level will be higher. Also, the airbags are not designed to inflate in rollovers, side impacts, or rear impacts, because inflation would not help the occupant.
It is possible that in a crash, only one of the two airbags in your vehicle will deploy. This is rare, but it can happen in a crash just severe enough to make an airbag inflate.
In any particular crash, no one can say whether an airbag(s) should have inflated simply because of the damage to a vehicle or because of what the repair costs were. For frontal airbags, inflation is determined by the angle of the impact and how quickly the vehicle slows down in frontal and near-frontal impacts.