They think the campaign affects the rate of boxes from chests when you open them with izzat/key.
Oh Great one can you translate their description?
- The number of lustreless scale boxes, lustreless hide boxes, and lustreless wing boxes acquired will be doubled.
Nynja already answered, but for your reference in the future when reading other documents, typically we read top-to-bottom and if there are indented sections with arrows, dashes, or bullet points it means these things are related to thing above.
Newly Added: The Great Odyssey Campaign
This part describes the campaign above
The following changes will be made to the rewards for reaching the Otherworldly Vortex in Sheol A, Sheol B, and Sheol C.
This part is giving more details about the thing above it
- Job points earned will be increased by 50%.
- Moogle Segments acquired will be increased by 50%.
- The number of lustreless scale boxes, lustreless hide boxes, and lustreless wing boxes acquired will be doubled.
Therefore: the Great Odyssey campaign -> Gives bonuses to the rewards for Otherworldly vortex -> Boxes will be doubled.
See? You can apply this knowledge to any number of other documents written in English, try it out!