The primary purpose of a payment gateway in e-commerce is to facilitate secure online transactions between customers and merchants. A payment gateway acts as an intermediary that encrypts sensitive payment information, such as credit card numbers, ensuring data security during transmission. It authorizes the payment by communicating with the financial institutions involved, allowing for seamless transaction processing. By providing a reliable, secure, and efficient method for online payments, payment gateways enhance customer trust and experience in e-commerce platforms.