Payburner creates two public and private key pairs to allow for encryption/decryption and signing/verification and stores the public keys on the XRP ledger. Like your Payburner account password and your XRP address secret, the private keys are stored locally in encrypted format and never leave your browser.
These key pairs are actually the bedrock of what makes Payburner great! How so you ask? So as we have explained Payburner users have publicly registered public keys for encryption and for signature verification. This allows for really cool features like automatic login to websites, end-to-end encryption when communicating with Payburner services. And much more. But this is a story for another day. We'll start leveraging and unveiling and discussing this key feature in the near future.
Clicking on Rotate Keys, creates a new set of key pairs and writes them to the XRP ledger using cost AccountSet transactions, which cost 10 XRP drops each.