If you've chosen valet parking, you'll always have to give them your car keys. You drive your car to the departures hall at the airport, where you will hand your keys to a member of staff from the car park. The car park staff member will drive your car to the parking space. Without handing in your car keys, this would be impossible.
When you choose shuttle parking, you'll need to drive your car to the car park you've booked. It depends on the car park as to whether or not you need to hand in your keys or not. The website will always tell you when you need to leave your keys. In most cases, you will need to hand in your keys if the car park has limited space and sometimes may need to move cars to create more space. The benefit of this is that you car will always be the one nearest to the exit.
Your keys are kept in a safe, so you won't need to worry about them getting lost or stolen.