First note that on later devices, Active Minutes have been replaced by Active Zone Minutes.
But for Active Minutes, it requires at least 10 continuous minutes at or above 3 METS (metabolic equivalents). 1 MET is resting energy expenditure, so 3 METS is basically burning calories triple your BMR (Basic Matabolic Rate).
For more detail and Fitbit's official explanation, see:
What are Active Zone Minutes or active minutes on my Fitbit device?
You will have to scroll down past the Active Zone Minutes sections.
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