Push Two-Factor Authentication using the Twilio Authy API allows users to securely access online accounts by receiving a push notification on their smartphone. This method simplifies the traditional two-factor authentication process, making it more user-friendly and increasing adoption rates. The implementation involves registering users for Authy push 2FA, generating QR codes that contain JSON Web Tokens, and waiting for the user to scan the code or tap the approval button in the Authy app. Once a user logs in with push 2FA enabled, the application checks if the user has approved the login request by calling the Authy API's one-touch send_request function and polling for an authentication response. If the user approves, the Authy service sends a push notification to their phone, which can be checked on the backend using the Authy client for Python.