Hyde here from Shopify!
The button you've highlighted on the product page is an example of a Dynamic Cart button checkout. It basically allows a customer to head straight to checkout, bypassing the cart itself.
Everything you need to know about creating and setting one up is listed in this help document. Of course, if you're using a third-party theme the setup may be a little different, so you will need to chat with the developers directly (you can usually find their details by going to Online Store> Themes> Customize > Theme Settings and scrolling to the bottom). You will need a credit card payment gateway too. We have a list here of all payment gateways that integrate with Shopify according to country.
I hope that helps. Happy to answer any other questions you may have.
All the best, Hyde.