What is cardDAV?

You don't need a cardDav.

Go into Settings->Mail, Contacts, Calendars->Accounts->Add Account . Tap on Gmail, and Enter all the infomation requested.

Once completed your Gmail contacts will appear in the Contacts App

The term "CardDAV" refers to a connection method or account type for syncing contacts, not a thing to get.

If I understand correctly that you want to use CardDAV to syncy your contacts to Gmail, follow this path:

Settings > Mail, Contacts, Calendars > Add Account... > Other > Add CardDAV Account

Then enter the server name, username, password, and a short string to identify the connection (like "CardDAV to Gmail") and hit the "Next" button.