Energy crystals made by Shinra.
These Materia are found throughout the game. The amount of them you could equip depends on the weapons you are using.
These Materia are similar to the Esper System found in Final Fantasy 7. It also have levels. Gaining a level make a materia better.
Summon Materia-
Your character will call and Magical Beast out to attack your enemies.
Go to the Summon Materia Section for more info!
Independent Materia-
It boost your stat, such as gaining more hp/mp!
Command Materia-
It gives you new abilities such as steal, check info on enimies.....
Support Materia-
It gives you specail abilities such as hit multiple enimies in a battle.