Materia system allows you to give traits to equipment. Each Materia has a level and EXP. If mastered, you get a new level one materia. Depending on certain combinations, you can have different effects. Here are some examples.
- ALL->ICE will make a single spell become an AOE spell for x times, depending on materia mastery. If All Materia is level one, you can only use this AOE-bonus 2-3x IIRC.
- Elemental Attack -> Ice, makes your attacks ice attribute.
- Final Attack + Phoenix, when a character is KO'd they will do a final attack. Phoenix is a popular combo for AOE damage+Revival.
They are divided into different categories.
But uh, here's from the wiki:
Materia can be used when slotted into a weapon or a piece of armor. Once slotted into an equipment piece the wearer can call upon the Materia's powers. Using Materia has both pros and cons. Depending on the type and strength of the Materia equipped, some stats may be hindered or enhanced. As an example, the "Restore" Materia picked up in Sector 1 Reactor at the beginning of the game reduces maximum HP by two percent and Strength by one, but raises maximum MP by two percent and Magic by one.
Winning battles earns Ability Points, which are Experience Points for Materia. Just like characters, Materia levels up when it gains enough AP. Some Materia allow access to stronger commands when leveled up, others allow the user to use the granted command more times, others give a stat bonus that grows larger. When Materia reached its highest level, it is "mastered", and a second Materia with the same powers is born. Thus, with patience and enough leveling up, even one-of-a-kind Materia could be reproduced infinitely.
Materia can be slotted into a single slot or a connected slot. When slotted into a connected slot, the Materia can be joined with a Support Materia to varying effects, including adding elemental properties to the slotted equipment, allowing the Materia to target multiple targets, etc. Some equipment affects Materia growth through AP; some have Materia slots but cause the Materia linked to it to gain no AP at all, while others double or triple the amount of AP. Other weapons and equipment have no Materia slots at all.
If the player's Materia inventory is full when trying to pick up a Materia piece the game will notify the player and ask them to remove Materia first. The Kujata Materia is an exception, and will be lost forever if the player picks it up with full inventory.
Leveling up a Materia to its maximum level, and leveling up all Materia to their final levels, gain the player the Master Materia and Materia Overload achievements respectively, in the PC version re-release version of Final Fantasy VII.
Red Summon Materia
Summon Used to summon creatures to aid in battle.
Green Magic Materia
Magic Used to cast spells, including Black, White, and status-inducing spells. Also affects Strength and Magic stats.
Yellow Command Materia
Command Allows the use of extra commands in battle like Throw and Steal.
Blue Support Materia
Support Can be linked to other Materia in order to enhance their effects.
Purple Independent Materia
Independent Various functions, including increasing stats and auto-abilities such as Cover.
In addition to the above, there is the unique Command Materia, the Enemy Skill Materia, which teaches Enemy Skills to the player.
More in-depth info over here:
http://allpoetry.com/column/7517767-Materia-System-Explained--Final-Fantasy-VII---by-Psi-rockin-beta
http://www.ffwa.org/ff7/materia.php