Your App Store settings may be configured to request a password every time an app is installed, for extra security, even for free download apps
If you have this extra layer of security configured on your account, then you will need to enter your App Store credentials to complete the App install.
✅ For Apple devices asking you to Sign in with Apple ID to authorise this transaction. You will need to enter your apple account password that matches the email address shown which is normally used in the App Store
✅ For Android devices, this will be your Google account email and password normally used in the Play Store
⚠️ If you don't want to enter a password, you can disable require password for free downloads on your iPhone
Android devices don't require passwords for free downloads