The Google Payments Center is likely one of the few Google sites that you rarely visit. It is a central location where you can see all of your payment information such as your recent purchases, your credit cards and shipping addresses, and your subscriptions that you have through Google. It is a site that, to be fair, you rarely need to use as most of the information in it can be found in the Play Store app or in Google Pay.
That doesn’t mean that Google doesn’t think it is important and over the weekend gave it a heavy Material Design makeover. The update was a cloud-side push as these things tend to go so there is nothing you need to do on your end. Just go to https://pay.google.com and you will be dropped into the new & improved Google Payment Center site.