The Power of Waking (眠りし心を解放する力 Nemurishi kokoro o kaihō suru chikara) is a ability introduced in Kingdom Hearts 3D: Dream Drop Distance and plays a key plot element in Kingdom Hearts III, described by Yen Sid as "the power to free a heart from its sleep". It is also one of the ways to safely access the Realm of Darkness, which Riku and King Mickey use in their efforts to find Aqua.
Story
Kingdom Hearts 3D: Dream Drop Distance
Sora manages to acquire the power of waking near the end of his and Riku's Mark of Mastery exam, but loses it when he is corrupted by darkness and nearly becomes a vessel for Xehanort. Riku then uses the power of waking to dive into Sora's heart and defeat the Armored Ventus Nightmare, saving Sora's heart.
Kingdom Hearts III
It was not until a clash with Vanitas in the Land of Departure that Sora is able to regain the power, using it to restore Ventus's heart to his body. After restoring himself in The Final World, Sora uses the power of waking to save his friends from the Lich, using it to travel from world to world and track each of his friends' hearts down. The young Xehanort warns Sora about using the power of waking this much, stating that it's meant to be used for "traversing hearts to reach worlds, not for traversing worlds to reach hearts," and that Sora using it as much as he does comes with a high price.
After the final battle with Xehanort, Sora uses the power of waking to revive Kairi, who had been destroyed by Xehanort, seemingly vanishing and becoming lost forever in the process.