The ActiveZoneMinutes (AZM) replaced the Active Minutes in the Fitbit Statistics to get a better overview about your active time over the day. The AZM is calculated depending on your current heart rate zone.
1 Minute in fat burn zone => 1 Active Zone Minute
1 Minute in cardio or peak zone => 2 Active Zone Minutes
For more information visit the fitbit help:
https://help.fitbit.com/articles/en_US/Help_article/1379.htm