An active payline in a slot machine is a line on which a player has placed a bet and can win payouts. These lines run across the reels and if the right combination of symbols lines up on an active payline, the player wins.
Paylines can be straight, diagonal, or even zig-zagging lines. The number of paylines on a slot machine can vary widely - some have just one, while others have hundreds or even thousands.
When playing a slot machine, you usually have the option to select how many paylines you want to bet on. The more paylines you bet on, the more chances you have to win - but it also costs more as the bet is per payline. If a winning combination lands on a payline that you didn't bet on, you won't receive a payout for it. So an "active payline" is essentially a payline that you've chosen to bet on.