The Payments Verified badge by a Sellers/Store name and on a listing teaser means that the Seller has been verified by Stripe and is accepting online payment for all of their fixed-price listings. If the badge is not showing on your listings, you will need to set up a (or link your existing) Stripe account to your Bazaar account.
To do this, head over to your Store Settings page and click on the Set Up Stripe Payments button. You'll be prompted to fill out a form with your personal and/or business information. Stripe uses this information to set up your Stripe Seller account and to verify you as a legitimate seller. Once you have successfully created your Stripe Seller account and authorized access for it, you'll see a Powered by Stripe Badge under Store Settings and the Payments Verified badge on all of your fixed-price listings.