Origin in the games
Little is known about the origin of the Master Emerald except that it resides in a shrine on Angel Island for an unspecified amount of time, guarded by Knuckles the Echidna. It was created by the gods, because they saw that people are using the Chaos Emeralds for evil, and equipped the gem to be able to negate the energy of the Chaos Emeralds. It has been in existence for thousands of years (at least since the time the Echidna clan was thriving) and has a large connection to the equally mysterious Chaos Emeralds, along with the being known as Chaos. It is also seen in Sonic 3 and knuckles in the middle of the Super Emeralds and again with Eggman taking it away from Knuckles and the Echidna jumping on to the emerald only to be shocked by the above mentioned villain.
The Master Emerald has unbound power, and is used to keep the Angel Island afloat in the sky. The Emerald also has the power to fully control everything that the Chaos Emeralds do. The Emerald also possesses the ability to both negate and empower Chaos Emeralds, meaning it can stop the energy of the Chaos Emeralds, or enhance them. The Master Emerald has also been seen creating three-dimensional holographic images within itself. And at times if damaged will make a person scream in pain and crack the chaos emeralds.
Only Knuckles, Chaos, Tikal,Chaos the Dark and Gus Chaos have been seen to be able to talk to, command, and control the Master Emerald.
Will the Echidna storyline
In the Will the Echidna series of fanfics by Flashfire212, the Master Emerald resides in a room in Knuckles' house.
Book One: The Beginnings
After this point, the fanfic is still under work.
Will, Maddy and Kyle are all in the lounge room in Knuckles' house for Will's birthday sleepover. Will couldn't sleep and heard someone in the Master Emerald room. Thinking it was his dad, yet not sure, Will walked down the corridor to find a Dark Legion member known as Jacob attempting to steal the Master Emerald. Will grabbed a sword with a Chaos Emerald Shard embedded in it's hilt and attacked Jacob, who pulled out a spear with a Chaos Emerald Shard in it as well and fought back. The fight was perfectly matched until Jacob Chaos Controlled into the lounge room where Maddy and Kyle were sleeping, then attempts to pull off her covers when he brushed against her skin, waking her and alerting Will who attacked him with Maddy when he managed to get back into the Master Emerald room. Will and Maddy follow him and attack him, with him defeating them. He then touched the Master Emerald and absorbed some of it's power into himself. He then Chaos Controlled away. Kyle, who had been woken when Jacob stood on him, Will and Maddy then touched the Master Emerald, absorbing power from it and establishing a link to it.
Book Three: The Invasion
After Scourge captured all the crystals he could, he and Striker went after the Master Emerald. Scourge went super. When they reached the Master Emerald room, they found Will was the only guardian. However, Scourge noted something was weird about his eyes. They were red, with black pinwheels for pupils. Scourge and Striker attempted to fight him, but even in his base form, he was moving almost three times faster than he should have been. He was also accurately predicting the future up to thirty seconds ahead. Scourge gave up, giving the fight to Striker, who was unmasked by a angry Will. By doing that though, he saw Striker's own single permanent Sharingan, and realized that it was Striker who killed Kyle, powering down his eyes and going shattered. Will then beats Striker as much as he can until Scourge Chaos Controls in, grabs Striker and goes straight to Moebius.
In this Universe it acts as one of the Seven Controllers,subordinates, toThe Vortex Emerald. Otherwise it's purpuose is exactly the same.
In Wh!te$tar's fiction, the Master Emerald doubles as a lock. Once one solves the puzzle around the Emerald, a passage below the altar opens, leading to the World Well, a chamber that reaches directly into Mobius' supply of Chaos energy. From here, that person has direct access not only to the whole planet, but also to Mobius' branch of the Inter-Cosmic Web.
Jezz of Time series (Bionicleboy3000's fiction)
In the Jezz of Time series, the Chaos Emeralds and the Master Emerald were all a set of stones called Gaia Stones, with the Master Emerald being the Supreme Gaia Stone. Over 5000 years before current events in the canon, an evil priest from a currently unknown echidna tribe tricked Jezz the Hedgehog into using his power on one of the Emeralds, which affected them all, turning them into the Chaos Emeralds we know today. Jezz doesn't think highly of this mistake.
The Master Emerald became the vessel carrying Umbra the Hedgehog's spirit around the time it became the Master Emerald, releasing Umbra in a living form the first time Jezz uses the Super Emeralds, 20 years after current events in the canon.
In this fiction, the Master Emerald doubles as a portal to the spirit world that only a master of all elements can use. If an element user who doesn't possess the ability of every element gets near the emerald, their powers completely neutralize until they are at least 100 feet away.