The Magic Hand is the seal that was set by Sheikah monks and Zonai mages 10,000 years ago, after reviewing Hyrule's history and discovering the repeating pattern of Demise's Curse.
With the Hylian King's permission, they successfully predicted when Ganondorf would return, sealing him when he rose to overtake Hyrule by using their own souls, accidentally causing the extinction of the Zonai tribe due to the loss of it's mages.
When Demise's Curse leaked out as Malice, the remaining Zonai were caught off guard and forced to hide underground, with the Sheikah building the Furnaces, Shrines, (which they encased the mummified Monks in) Guardians, and weapons using Ganondorf's spirit energy to power it to help keep the seal going.
When Mummydorf morphed the Malice into Calamity Ganon, a Hero was found, and the Malice Pig was defeated with the Zonai becoming extinct and their descendants turning into the residents of Lurein Village.
Afterwards, the Hylian King exiled the Sheikah, fearing their technology, and the Yiga Clan was born.
After Malice Pig is sealed, the power it amassed returns to Mummydorf, weakening the seal immensely.
The spirits panic, sending a call to Link and Zelda, prompting them to look underneath Hyrule Castle.
In BOTW 2, Zelda and Link find a massive Zonai cave/temple under Hyrule Castle.
They explore, finding Zonai ruins and thousands of Luminous Stones.
Eventually, they stumble upon Mummydorf. An earthquake happens, with Zelda falling off the cliff, Link falling off to save her, and the Magic Hand releasing Mummydorf to save Link.
Zelda is returned to solid ground, but she witnesses the revival of the Demon King.
Said Demon King releases a massive amount of Malice, targeting Zelda and Link. Zelda's somewhat fine due to her using her remaining power, and Link is launched into another bit of the cave after the Hand made him absorb it.
After we watch this cutscene, Link wakes up, and we see this message:
"You survived due to the mysterious hand, but all of your items are gone and Malice has stolen your vitality!" (Or something like that)
Through the game, we find Shrines or Fairy Fountains who can restore our power, bit by bit as we rescue them from the Ganon Goo.
We also gain abilities from the Hand, (like the Champions Gifts or the Runes) which also acts as a guild. Like Z-Targeting and pressing a button, and the Hand will give information, like Fi in Skyward Sword.
