When somebody invites you to their Timekit app they either set a password for you or invites you via email to set your own password. In either case, when you log in you are ready to go - fully powered by Timekit.
Why sync with Google?
While you don't need a 3rd party calendar service to offer bookings from time to time it can make sense to sync Timekit with a Google calendar. It enables you to find availability in your personal/work calendar and to save booking received to it. This can be beneficial if you are using your calendar for other appointments/events than those created through Timekit.
How to set up sync?
Navigate to your account settings, select the 'Calendar sync' pane, then simply press "Sign in with Google" and login. That's it! Afterwards you can select which of your google calendars you want to sync.
If you don't have a Google Calendar you can get one for free here: Get Google Account or visit the professional version called G Suite here: Get a G Suite Account