"Authority to Leave" means that you are happy for the delivery driver to simply leave the parcel unattended at the delivery address if no one is in attendance when they arrive.
When you complete your order in the checkout you will be the given option to leave order comments and this is where you let us know if you are happy for this to happen.
Giving authority to leave is convenient where you find yourself unable to be at home and are also unable to come up with an alternative delivery address (Like your work or your partners work, or a trusted neighbour).
A portion of customers give us authority to leave when placing their orders and it is rare for this method to introduce complications in the process. However, it is important to consider that we cannot be held responsible, in any way, for any deliveries where you have given us authority to leave. Unfortunately, things can happen to an unattended parcel that is totally outside of our control - It might be that it is "liberated" / damaged/tampered with by a nefarious passer-by, or simply left in the sun/rain / near an animal with a bladder control problem, or otherwise.