From Sonic Retro
The Master Emerald contains an immeasurable amount of power which is used to keep Angel Island afloat in the sky. It also possesses the ability to negate the effects of the Chaos Emeralds.
Role in the Story
The scene originally thought that the green emerald in the Sonic 2 version of HPZ was the Master Emerald, but the interview with Craig Stitt revealed it was supposedly nothing more than a breakable block.
Sonic 3 & Knuckles
The Master Emerald appeared again in Sonic Adventure for the Sega Dreamcast, where it was again shown keeping Angel Island afloat. The emerald also held within it the ancient monster known as Chaos. In the game, it was shattered by a mysterious force, causing Angel Island to fall.
Sonic Adventure 2
The Master Emerald was again a source of contention as Knuckles fought with Rouge the Bat for possession of it. Eggman tried to steal it again while they were distracted, but Knuckles voluntarily shattered the Emerald in order to keep it out of his hands. Knuckles and Rouge then set off seperately to gather the shards of the emerald for their own reasons.
The Master Emerald in the Archie Comic
The Brotherhood is a group of echidnas in charge of protecting Angel Island. Knuckles is a decendant from these male echidnas, and is now guardian of the island, doing what his ancestors have done for quite a bit of time.
Tikal found Chaos and the Chao in her ancient echidna family. She loved them and cared for them, but her father found out about them and wanted the power of the chaos emeralds for himself. He attacked the emeralds and tried to steal them for himself, but Chaos absorbed the power of the Emeralds and became Perfect Chaos, before Tikal appealed to the Master Emerald to seal Chaos away inside it, sealing herself in the process. We know this because Tikal's spirit is of the age when she was sealed, which is the age at which her father attacked the emerald. The Chao lived on and bred, however.
This is the point at which the echidnas took over in protecting the emeralds. Knuckles is the echidna that protects them in the time of the current Sonic the Hedgehog timeline, and probably the only echidna left (In the Sonic Team storyline, adaptions like the American Sonic comics have more echidnas in existence).
It is not known if the island was afloat in the time of Tikal. The geography of the island in the past and present seems to indicate that it wasn't afloat in the time of Tikal, as the Emerald shrine was directly connected to the Echidna city in the past, but now they're seperate. It's possible the floating island was created when Perfect Chaos arose before Tikal sealed him.
Chaos Emeralds in the Comics
In Fleetway's Sonic the Comic, the history of the Emeralds is expanded considerably, though some points contradict the storyline of the games. The Grey Emerald is said to be the most powerful of the seven, and has the ability to control the energy of the other Emeralds. However, the Master Emerald can still over-rule its power. The original form of the seven Emeralds were what is now known as the Super Emeralds. They were taken from Angel Island by persons unknown (though it was probably Dr. Ovi Kintobor, the original form of Dr. Ivo Robotnik) and began to lose their power, reverting to the small emeralds that are familiar to all the Sonic games. Dr. Kintobor planned to use the Emeralds as a storage device to contain all the negative energy in the world, but a freak accident infused him with pure chaos energy and turned him into Sonic's lifelong antagonist.
In the Fleetway comics (and contrary to Sonic Adventure), there is no positive energy in the Emeralds; only chaos energy. The Emeralds absorb chaos energy through contact, draining the victim and growing more instable. In contrast to this, Sonic absorbs chaos energy, which is why he is the only one (storyline-wise) who is able to harness their power and transform into Super Sonic. The only way to stop the transfer of chaos energy to and from the Emeralds is to keep them at a cold temperature. In the comic, Super Sonic was an insane, all-powerful version of Sonic created when he absorbs too much chaos energy and goes out of control.
It is also implied that it was the Emeralds which created the Special Stages in order to protect themselves from Dr. Robotnik. The comics also claim that the seven original Emeralds were split into fourteen - the emeralds from Sonic 2 and Sonic 3 respectively. These Emeralds were then fused back into seven in the comics. However, this is never proven or implied in the games.