Final Fantasy VII
Shrouded in mystery and known to very few people, the Black Materia remained untouched since the time of Jenova and the Ancients. Many believed it was hidden in the depths of the Temple of the Ancients, but this isn't entirely true.
When the materia is not transformed, it instead takes up the shape of an Aztec pyramid, the materia is the Temple of the Ancients. Upon being activated from inside, the materia then changes to a spherical ball, much more familiar compared to other materia. It's also worth noting that while it is referred to as "Black Materia", when the light hits it, the colour can change to dark blue or purple (as show in the screenshot above).
How Sephiroth Acquires The Black Materia
When Sephiroth fell into The Lifestream and remained dorment there, he learnt of the Black Materia's incredible power. It was here that he began his plot to claim it, and then use it in order to achieve what Jenova had failed to do before.
When Cloud Strife and the others arrive at the Temple of the Ancients, they learn deep inside that the Black Materia is infact the Temple itself. This was something that the Cetra devised to stop people being able to use the Black Materia, as it shrinks to a fraction of the size, crushing all those inside. When Cait Sith solves the puzzles inside the temple, only then does it transform into a more suitable size. However, his body is crushed inside the temple when it shrinks. Cloud is then manipulated afterwards by Sephiroth, who forces him to hand over the Black Materia.
Sephiroth Summons Meteor
Cloud decides to give it the Black Materia to another party member, so that he can't be manipulated by Sephiroth. However, when the party defeats Jenova DEATH at the whirlwind maze, Cloud is manipulated again, ultimately giving the Black Materia to Sephiroth.
After finally acquiring the Black Materia, Sephiroth uses it to summon Meteor. The materia is then lost in the centre of the planet.
Final Fantasy Tactics
Black Materia makes an appearance in a somewhat different form in Final Fantasy Tactics. Appearing as stones developed by ancient Saronians, it is claimed to enhance the abilities of anyone who possesses it. In reality, it's a relic that is included in the game to pay tribute to Final Fantasy VII.
Black Materia can be obtained in Final Fantasy Tactics by completing one of the Errands.
Dissidia: Final Fantasy
The Black Materia appears in one of Sephiroth's HP attacks, whereby he uses it to summon a meteor from the sky.