King Drasil

Yggdrasil is the name of a fictional character in several iterations of the Digimon franchise, named after the world tree from Norse mythology. He primarily factors into the backstory written for the Digimon virtual pets and card game, which is a background storyline that is less prominent and often contradictory to the various anime. He appears as a character in Digital Monster X-Evolution and Digimon Savers.

In the continuities he appears in, Yggdrasil is always displayed as a "god" unto the Digital World, the otherworldly realm home to all Digimon. Yggdrasil oversees the Digital World's surival and, in some cases, destruction. Bandai calls him the "Control Computer of the Digital World", but in both of his animated appearances, his true nature is somewhat more ambiguous.

In all continuities he appears in, Yggdrasil has command over the thirteen Royal Knights.

Digital Monster X-Evolution
In the animated movie, Digital Monster X-Evolution, which is based on the Digimon Chronicle storyline created by Bandai in conjuction with the Pendelum X virtual pet and card game, Yggdrasil has, for some reason, set off a chain of events that has resulted in the destruction of the original Digital World and the creation of a new one, inhabited by the select few Digimon that Yggdrasil has hand-picked to survive. However, Digimon who survived the death of the old world by way of the mysterious "X-Antibody" have appeared in this new Digital World, disrupting Yggdrasil's plans.

For reasons unknown, Yggdrasil ordered his Royal Knights to exterminate both the "X-Digimon" as well as the Digimon he had chosen to survive. Using the data of the digimon known as Dorumon, Yggdrasil created a vast army of digimon called DexDoruGreymon, as well as his personal protector, DexDorugoramon, who later became Dexmon. The Royal Knight Gallantmon turned on him, believing his intentions to be wrong, and after becoming an "X-Digimon" himself, he sent Dorumon to his comrades, Omnimon and Magnamon, in an attempt to bring an end to the fighting.

In the Royal Knights' stronghold, Dorumon was revealed to be Alphamon, the legendary leader of the Knights. This was enough to convince Omnimon to face Yggdrasil, and he went with Alphamon to seek counsel with his master. Yggdrasil used DexDorugoramon and violently rebuffed them, but they made it to him nonetheless. When Dexmon emerged and attacked them, Alphamon sacrificed himself and impaled both himself, Dexmon, and Yggdrasil with his own weapon.

Reverting to Dorumon, Alphamon left the resolution to Omnimon, giving him his own X-Antibody. Yggdrasil's plan to destroy the new Digital World had almost been completed, and so, Omnimon struck his master down with his "All Delete" attack, destroying Yggdrasil and allowing the Digital World to be reborn.

Later, Omnimon and Gallantmon speculated on Yggdrasil's intentions. For all that he had done, a reason remained unclear to both Knights - but in the end, Gallantmon speculated that Yggdrasil had, just as all Digimon had been, fighting his own destruction. What this means is unknown, but it hints that Yggdrasil acted out of desperation.

Digimon Savers
In Digimon Savers, Yggdrasil is a pivotal figure in the storyline, particularly in the show's final storyarc.

Yggdrasil is first mentioned by Mercurimon, who, ten years before the start of the series, told of Yggdrasil's existance to Suguru Daimon, the father of series' protagonist Masaru Daimon. Suguru and Mercurimon departed, with the former stating that he would seek out Yggdrasil himself.

Years later, it seemed that Suguru had found Yggdrasil - in more ways than one. With the Human and Digital World poised to collide due to the schemes of Akihiro Kurata, Masaru and his comrades sought Yggdrasil in order to try and find a solution with him. They met not only Yggdrasil's Royal Knights, but Yggdrasil himself - in the form of Suguru Daimon.

"Suguru" had no memory of his former life or his family, and ordered the destruction of the Human World in order to save the Digital World, sending his Royal Knights out across the globe to destroy it. Masaru resolved to discover the truth of what his father had become, and embarked on a quest to find Yggdrasil again.

These events are as of yet unresolved.

Trivia

 * Though Yggdrasil is relatively new to the Digimon mythos, a similar character exists in the Digimon Adventure and Digimon Tamers continuities named ENIAC. ENIAC, as the first computer, laid down the foundations of the Digital World, and because of his unique nature, he exists in multiple universes all at once.  ENIAC appears only in the series of games starring Ryo Akiyama for the Wonderswan, and is part of one of Ryo's attempts to defeat the evil Millenniummon.  As an added note, ENIAC's appearance in the game, as a clear orb sitting upon a pedestal, is practically identical to Yggdrasil's appearance in X-Evolution.