A payment gateway is what allows you to accept payments. If you’re not offering all your products for free, you’ll need one. WooCommerce comes with a PayPal payment gateway built in, but if you don’t have PayPal or prefer a different payment gateway, that’s not a problem.
You can install plugins for other payment gateways by going to WooCommerce, then Settings, then Checkout. There you can find other payment gateway options.