This feature allows you to capture the responses received from the Braintree gateway when sending a payment transaction request. Usually you would want this when you want to debug the way that this plug-in works.
The debugging works at two different levels: on the server-side where the payment requests/responses are handled and on the client-side from the “Place Order Now” click to the “Thank you for order” post-order notice. At the server level the debug messages are stored in a dedicated log file that usually can be found at wp-content/uploads/wc-logs/Braintree-xxxxx.log. At the client level the debug messages are only printed in the browser console so after the browser is closed they are not stored anyware. If you don’t know what the browser console is and how to activate it then just search “browser console firefox” on Google (or Chrome, Internet Explorer, Opera) and you will find many good articles explaining that.