In Xconq, materials are basically bulk inanimate stuffs, like food or fuel. They are kept in units or in cells, up to limits defined by the game. Materials may be provided as part of the initial game setup, or else produced by units and cells. They are consumed by construction, movement, or merely in order to survive. You can also move materials around from unit to unit. Some games define laws of supply and demand, which will move materials for you, though not necessarily in the directions you would prefer!
In a few games, possession of a material type may figure into your score (gold in a dungeon-type game, for instance). In other games, there are no types of materials at all. Sometimes materials exist only to constrain units' actions, such as fuel to prevent airplanes from straying too far from airports, and so you may not need to do much with the materials yourself. The player notes and help info for the particular game should explain this if so.