Certain weapons and armor in the game contain single and paired Materia slots as shown below:
You can pair Materia with Support Materia (the blue ones) in the paired Materia slots. Each Support Materia has a different effect on the Materia that you attach it to and this is not necessarily limited to just Magic Materia. The effects can be applied to most Magic Materia, some Command Materia and some Summon Materia. A few examples are listed below:
All Materia Probably the most important Support Materia in the game. This Materia allows for quick and easy healing of allies with low health early in the game, and Restore Materia should always be paired with an All Materia (unless of course you have a Mega-All Materia, which you have access to much later in the game). All Materia also gives you the ability to attack every enemy in the battle with one use of a Magic Materia (as long as they're paired together in the same slot of your armor). Because you're given access to quite a few All Materia in the game, equip one to a Restore Materia and use the rest for offensive spell casting. Just make sure to check that the Magic Materia you've paired the All Materia with doesn't automatically hit every enemy on the field already (for example, Ultima Materia hits every enemy on the field without the need for a paired All Materia).
It can be paired with the following Materia: Restore, Heal, Revive, Fire, Ice, Lightning, Earth, Poison, Gravity, Seal, Mystify, Transform, Time, Barrier, Destruct, Master Magic
Added Effect: Can be linked to some Magic Materia and some Summon Materia. If you pair it on your weapon you have a 20% chance of inflicting a status effect on an enemy when you use a regular attack. If you pair it on your armor you can make a character immune to specific status effects.
It can be paired with the following Materia: Poison (Bio), Seal (Sleep, Silence), Mystify (Confuse, Berserk), Transform (Mini, Toad), Time (Haste, Slow, Stop), Destruct (Death), Contain (Confusion, Stop, Petrify), Choco/Mog (Stop), Odin (Death), Hades (Sleep, Poison, Confusion, Silence, Frog, Mini, Slow, Paralysis).
Counter Materia: This Materia is not the same as Counter Attack Materia. Counter works by attacking the enemy with the paired Materia after the character has been attacked. It starts off with a 30% chance to activate, and improves up to a 100% once the Materia has leveled to level 5. Read the fine print though; "Attacks with paired *Command* when damage is incurred". This indicates that you must use Command Materia, rather than Magic Materia, in order to activate the effect. This includes the following Materia:
Deathblow, Master Command, Manipulate, Mime, Morph, Sense, Steal, Throw
Note: When paired with Master Command Materia, which gives you access to every Command in the game, a random Command will be chosen and used when the Counter Materia is activated.