Activity Rules allows for the triggering of a new Activity Process based upon how an Activity is resulted, and also choose what the Activity Reference needs to be (if applicable). These are used heavily in Call Center, but can also be very useful in a non-call center setting as well. An example would be if there was a Call Out Activity scheduled to confirm an appointment with a lead. They don't answer, so a message is left. Now another Activity is needed so that the lead get's called again in the future. It could be set up so that the new Activity Process is triggered based upon the result of the previous Call Out Activity.