"so that he'll fill the sacks along his backbone with air"

Fish Swim Bladder
Creative Commons Attribution Share AlikeFish Swim Bladder - Credit: Algirdas
Santiago is referring to the fish's swim bladder, the lung-like structure that allows ray-finned fish to control their buoyancy:

 

"Blue marlin have an unusual swim bladder in the form of a thin-walled, multichambered sac extending from the level of the first pectoral fin to behind the first anal fin. Observations of marlin 'finning' near the surface with the dorsal and caudal fins high above the water show that the bladder is large enough for the fish to be positively buoyant near the surface."

(from DIRECT MEASUREMENT OF SWIMMING SPEEDS AND DEPTH OF BLUE MARLIN by BARBARA A. BLOCK, DAVID BOOTH)