A 'three day inspection' is a commonly used convention in auctions and other situations when the buyer cannot physically examine the firearm prior to committing payment. It allows a purchaser of a firearm to physically inspect the firearm at the local transfer agent's facility prior to completing delivery (logging it out of the local FFL/transfer agent's bound book). It is not controlled by any law or government entity, and is not a specified or mandated service.
In practice (for an auction win, for example), you send the purchase money to the seller and they ship the weapon after payment clears. The 'inspection period' starts the day that the local FFL receives the transferred item. Within that period of time, you have the ability to go to the local FFL and physically examine the firearm. If it meets your expectation, you complete the transfer. If not, you can pay the FFL to send it back to the seller and get your money back. Return shipping costs are usually borne by the buyer.
Virtually all 'three day inspections' are non-shooting inspections, to ensure that the firearm doesn't get dogged during inspection and then summarily returned with more wear-n-tear than when it was sold/shipped.
It is a form of protection for the buyer, in that it at least allows the buyer to examine the firearm for blemishes, wear, and other such things. There is a presumption that the buyer is capable of looking at the physical characteristics of the firearm and determining its condition, but that's really no different that how you'd go about buying any used gun.