Why is Calendar asking for my Google password?

The Calendar App on Apple devices can show Google calendars. If you have a google account setup and the Calendar option turned on for it, it will require the account's password to access the Calendar.

Go to Settings ➜ Apps ➜ Calendar ➜ Calendar Accounts and check if you have added a Google account / Gmail there. If you don't want it, you can remove it or turn off the Calendar option there.

Is this a google calendar asking for your google password? If so, please contact google for help. Or, since this seems you are asking about the Caldav calendar. In that case, contact their support. Apple does not support third party apps.