[Arm] is a setting on an area level that activates the alarm of an area when there has been an unauthorised access. [Active] is when a zone is in an armed state where an alarm could be triggered.
In other words, since areas are made of zones, when an area is armed that means that all its associated zones are armed. And when there is activity in any zone, the zone will display this as "active". So if a zone in an armed area is "active" without a bypass, then the alarm will trigger for the area as a whole.