Active response methods are ideal for use in situations where you would not want a method to run repeatedly for the same incident. For example, restarting a service or device.
Non-active response methods execute every time the action group they belong to is automatically run by the incident. But, active response methods will only execute the first time their action group is automatically run by an incident. (Note that active response methods will always execute when their action group is run manually by a user from within the Incident View dashboard.)
See Action Groups for more information.