I'm really interested in this detail since saltine crackers aren't exactly what we today think of as an especially desired food.
Here's a link to the relevant scene, which is timestamped.
In the Pacific War, Saltines were NOT considered valuable unless troops had been starved for months. The scene in "The Pacific" is designed to show just how desperate Robert Leckie and the 1st Marines were for food. This situation is not typical for the Pacific War, it's an unusual circumstance of the Guadalcanal campaign.
When the Marines landed on Guadalcanal in August, the Imperial Japanese Navy swiftly counterattacked. Their naval forces, operating at night, won the battle of Savo Island and controlled the seas around Guadalcanal during the night when aircraft could not effectively contest them. During the day, aircraft operating from the airfield at Guadalcanal were able to contest Japanese control of the sea. This created a supply situation where the U.S. was only able to land or fly in a small amount of supplies each day before having to retreat in the face of Japanese nighttime seapower.
The U.S. Marines soon began to suffer from lack of supplies. Fuel and Ammunition had to be prioritized above food to keep the supply lines open and the perimeter around the airfield intact. The Marines main source of calories was a stockpile of rice captured from the Japanese in August. This rice soon became unwholesome in the tropic conditions, and in short supply. The daily ration was two tablespoons of rice at one point. Many Marines lost up to 40 pounds, and they were depression era men who began the war much slimmer than Americans are today.
Naval attempts to break the Japanese nighttime sea control failed until mid-November, when a pair of U.S. Navy battleships equipped with radar won a night battle and broke the IJN control of the seas at night. Thereafter the U.S. navy could effectively supply the marines.
"The Pacific" tries to show the short rations, but two hours of television can't capture the desperation of three and a half months of starvation rations and harsh conditions.
Why is a box of saltines so valuable to the Marines who had been starving for months? It's familiar food. It's high calories. It doesn't have to be cooked to be palatable, and hasn't been made unwholesome by tropic conditions. The canned peaches they trade for are pretty much the same sort of thing, food only rendered valuable by the months of starvation.