In this context, average means loss.
General Average is an old concept in maritime law. If your goods are being carried by sea and they have to be sacrificed in an emergency so that the ship and all the other cargo make it to a port, the owners of the ship and cargo that are saved have to contribute to pay for your loss. So, everyone involved suffers a general loss. Everyone also needs to pay for the salvage costs, which can be substantial if the ship is rescued when at sea.
A ship owner may declare General Average after a major incident that incurs losses. The costs can be significant – as much as 40% of the value of the cargo that will have to be paid in addition to the usual freight costs. General Average is usually an insured peril under marine cargo policies.
The ship owner will not release goods until the cargo owner has paid a deposit for the General Average or provided some other acceptable form of security such as a bond. A cargo insurer can provide this bond and have the goods released to your client as part of the insured cover.