Airbag control modules from 2007 and on evaluate sensor data and deploy when doing so is less dangerous than injuries from the accident. In general, this threshold is equivalent to hitting a rigid wall at 10 to 12 miles per hour if the occupants are not wearing seat belts.
For belted occupants, the threshold is roughly 16 miles per hour because the belts alone provide sufficient protection. If the sensors recognize that the occupant is a child or small adult, bag deployment can be delayed or modified. Most accidents aren't into fixed rigid objects though, and any movement or compression of the object struck decreases the likelihood of airbag deployment.