The Korok Forest is a location in The Legend of Zelda: Breath of the Wild. It is the home of the Koroks located in the region of Great Hyrule Forest. The Master Sword can be found here guarding by the Great Deku Tree.
Great Deku Tree
The Great Deku Tree can be found in the middle of Korok Forest. The Korok that live there live both in and around the Great Deku Tree. To call Korok Forest a village is a bit of a stretch as it lacks buildings or homes as the Koroks apparently prefer to live in a natural setting. In fact according to Maca the shops and inn where added in anticipation of the Hero Link's return and which implies that Korok Forest did not originally have shops or an inn.
In a small hollowed out room inside The Great Deku Tree, Link can find a Mushroom Shop called Spore Store, the General Shoppe which functions as Korok Forest's General Store, and an inn called Great Deku Tree's Navel. According to Natie, this hollowed out room is actually The Great Deku Tree's stomach, which is ironic considering there is a cooking pot in the middle of the room.
Link can also climb the Great Deku Tree where he can find a small grove and the Korok Walton who gives him the side quest "Riddles of Hyrule". Fairies can also occasionally appear on top of The Great Deku Tree near Walton as well.
Master Sword pedestal
When Link first enters the forest, he spots the Master Sword in its pedestal within Korok Forest and the Great Deku Tree speaks revealing that he has been waiting for him to appear and that the sword is his to take, though warns him that the Master Sword will test him to prove he strong enough to wield it. When Link attempts to pull it out, the Master Sword will sap his hearts as he pulls killing him if he runs out of Hearts before removing it. The first time he tries this the Great Deku Tree will stop him if he does not have enough heart containers, however subsequent attempts will kill him if he doesn't stop before he runs out of hearts. Link must have at least 13 hearts (yellow extra hearts do not count) to pull out the Master Sword and obtain the legendary Blade of Evil's Bane. Link can do this at any time after he has reached Korok Forest and has a health gauge with at least 13 hearts, thus he can obtain it pretty early on even before completing "Seek Out Impa", however it can only be done after "The Isolated Plateau" as he must leave the Great Plateau.
After removing the Master Sword from its pedestal, Link receives a vision showing Princess Zelda brought the Master Sword to the forest for safekeeping and spoke with the Great Deku Tree, after Link was sealed within the Shrine of Resurrection during the Great Calamity events. Zelda reveals to him that she heard the Spirit of Master Sword telling that her destiny was not finished. Zelda then places the Master Sword in its pedestal and leaves to seal Calamity Ganon in Hyrule Castle.
Back in the present, the Great Deku Tree reveals what Link saw was a vision and states the Master Sword is a divine weapon, though warns Link of over relying on its power. He also states that he hopes to see Princess Zelda's smile once more.
Trial of the Sword
During "EX Trial of the Sword" from The Master Trials DLC, a mysterious voice tells Link of a glorious trial and instructions him to seek out the Great Deku Tree to learn more. Upon approach the pedestal or the Deku Trees face, a cutscene is triggered in which the Great Deku Tree explains that the Master Sword has yet to realize its true splendor and that this trial shall test Link's courage to ensure he is worthy of this splendor. During this trial, Link will be unable to use the equipment, armor, and items he has come to rely on. Only the Paraglider, Sheikah Slate, and Runes shall be retained as all of Link's Champion abilities, Armor, weapons, bows, and shields he has obtained will be sealed during the trial forcing Link to rely on his runes and any equipment obtained during the trial. Additionally, Link's amiibo Rune cannot be used during the trial. The Great Deku Tree tells Link to place the Master Sword back in its pedestal to begin the trial. After doing so, Link is transported to a shrine-like area full of enemies. Defeating these enemies will activate a warp pad that transports Link to the next floor. The trial is separated into three parts each with a number of floors he must complete. When the first part is completed, the Master Sword's attack power is increased to 40, completing the second part increase it to 50, and completing the third and final part will unlock its glowing "True" power state permanently putting the Master Sword's attack power at 60 and boosting its durability (it will still need to cool down when its energy runs out and its cool down time remains the same). As it is a DLC side quest, this side quest is entirely optional.