A private label credit card is one where a merchant issues a card with a unique design and logo on it. This is different than a store card because many store cards can only be used in house.
Private label cards often share a logo with Visa or MasterCard, extending credit elsewhere. The reason a company may engage in this practice is because it helps differentiate itself. When customers pull out their card to pay for something at the grocery store with an exquisite Vive Paris card, it gets noticed because of its pretty design and differentiation from the crowd.
In addition to this, businesses can offer rewards to those who use the private label card in their store, encouraging more purchases and customer loyalty.