When things or people are inactive, they're doing little or nothing. A rock, a couch potato, or a gym membership you haven’t used yet is inactive.
Active has been used since the 14th century to mean "given to worldly activity." If you’re active, you’re out in the world! Therefore inactive people aren’t doing much. Maybe they’re just taking a break — if a player is inactive for a basketball game, she's sitting on the bench. In physics, an inactive object is motionless. If a club is inactive, it hasn't met for awhile. When things are inactive, there's not much going on.