Moon Stones are special items that are required to explore any unburied Golden Pyramid during Expeditions 4, 5 and 6. An unburied pyramid will require 1 stone in Expedition 4, or 2 stones in Expeditions 5 and 6. These stones can be commonly found in shrines and tombs starting in Expedition 3. They can be kept and brought to future expeditions, so it's wise to save them even if the current expedition's pyramid doesn't require them.
You must have any required stones on your person when exploring the pyramid for it to open. This means any stones left in a mission or polar station will be useless to you when you approach the pyramid.