The Master Emerald doesn't play an important role in the early part of Sonic X. However, after a giant Chaos Control brings the worlds of Sonic and Earth together, it appears on Earth along with Angel Island. It is then shattered by the release of Chaos, leading to Knuckles' search for the fragments across various areas, based on the plot of Sonic Adventure. Following the game's plot further, it served to contain Chaos and Tikal, shows certain individuals visions of the past, and is eventually put together.
Later, the anime adapts Sonic Adventure 2, and the Master Emerald is stolen by Rouge the Bat (unlike the game, it is never shattered) and taken to Space Colony ARK. Knuckles follows and battles her, and wins the Emerald back. Later, Knuckles uses it to drain the Chaos Emeralds of power, shutting down the engines that propel the colony towards the planet.
In the second series, the Master Emerald first serves as the power source for Christopher Thorndyke's crossover into Sonic's world. As a result of the time difference, the six years Chris has aged back in his world are stored inside the Master Emerald, returning him to his childish appearance, at least that was Eggman's theory. The Master Emerald also serves to power the Blue Typhoon space ship, which Sonic and co. use to travel around the galaxy and battle the Metarex. It's most important use is to power the Sonic Power Cannon, a massive cannon that is one of the few weapons effective against Metarex. The Master Emerald is left shattered and powerless after an attempt to use the Sonic Power Cannon to destroy Metarex leader Dark Oak. Oak absorbs the energy and fuses with Chaos, while Chris' age data is corrupted, preventing him from returning home through that method.