After you cancel, you keep Premium until the end of the period you already paid for. Then your account returns to the free tier.
Your account, bookings, documents and messages are not deleted. Premium features show an upgrade screen. You can subscribe again at any time.
The introductory prices apply once per person, so a new subscription later may start at the standard price. The app shows the price before you confirm.
To remove your data completely, see delete your account. Note that deleting the account does not cancel a store subscription: cancel it first (iPhone, Android).