The checkout question — do you have a Bonuskaart? — tends to arrive before newcomers know what one is, and the paid Premium subscription is pitched separately on top of it. The two are easy to conflate, and only one of them is free.
The Bonuskaart is Albert Heijn's free loyalty card — scan it at checkout and you unlock bonus-folder pricing plus increasingly personalized deals based on your purchase history, which is also the privacy trade-off worth knowing: AH uses that data for targeted offers and marketing, same as most supermarket loyalty schemes. It costs nothing and there's little reason not to carry it if you shop there regularly. AH Premium is a separate paid monthly subscription on top of that, running somewhere in the mid-teens of euros, and it buys a standing 10% off all AH huismerk products and the AH Terra plant-based range, free delivery above a lower spending threshold, and extra personalized offers. The math only works if you're already a loyal, frequent AH shopper who buys a lot of store-brand groceries rather than A-brands, and who orders delivery often enough that the free-delivery perk actually gets used. If you split your shopping across Lidl, Jumbo, and AH, or mostly buy branded products the discount doesn't touch, the subscription fee will likely cost more than it saves — worth tracking a month of receipts before committing.