Final Fantasy VII
White Materia is a very unique form of Materia, and is the direct opposite to Black Materia. The White Materia is used by Aerith Gainsborough to speak to the Planet. To signify that this action has happened, the Materia glows green.
The materia itself was used to summon Holy, which embodies the power of the Planet in attempt to protect itself. The White Materia was given to the Cetra by the Planet, along with the Black Materia. However, the Cetra sealed the Black Materia away as it could easily be manipulated. As the Cetra's numbers began to dwindle so did the knowledge of Holy. When Ifalna passed away, she gave the White Materia to her daughter Aerith, but was unable to explain its potential to her.
When Aerith was travelling with Cloud and the others she learnt about the White Materia's abilities, and with that knowledge she knew she was the only one who could actually stop Sephiroth's plan. She head to the City of the Ancients in order to meditate, with the hope of summoning Holy. Sadly during this she was killed by Sephiroth and the White Materia falls from her the hiding place inside her hair and bounces down the steps into the water.
Aeris' prayer was not in vain however, as her words were heard by the Planet. Despite this, Sephiroth was preventing the Lifestream from answering.
When the party defeat Sephiroth, Holy was finally able to prevent Meteor from destroying the planet in conjunction with the Lifestream.
Final Fantasy Tactics
Final Fantasy Tactics sees players obtain an artefact from an Errand called White Materia. However, it serves no purpose other than acting as a memento.
Dissidia: Final Fantasy
The White Materia appears in Dissidia at the end of Cloud's story. He acquires it after defeating Sephiroth in the Northern Crater.