Guidance Stones are items from The Legend of Zelda: Breath of the Wild. There are several Guidance Stones found within certain Shrines, in every last Sheikah Towers, the Hateno Ancient Tech Lab, and the four Divine Beasts. They have varying functions depending on where they are located, and they all require the Sheikah Slate to function.
The first Guidance Stone Link encounters is found in the Slumber of Restoration chamber where Link awakens. Accessing this Guidance Stone will reward Link with the Sheikah Slate and open the chamber's door allowing Link to venture further into the Shrine of Resurrection. In order to leave the Shrine of Resurrection Link must activate a second Guidance Stone, which opens the door that allows Link to go outside to the Great Plateau. During "Follow the Sheikah Slate", Link is directed by Princess Zelda telepathically to follow his Sheikah Slate, which leads him to another Guidance Stone. This Guidance Stone turns out to be the Guidance Stone for the buried Great Plateau Tower which ends up activating the tower, causing it and other towers to raise from the ground all over Hyrule and causes the Shrines to activate as well, though they remained locked and some remained buried or concealed.
The Guidance Stones within the four Shrines of the Great Plateau region are used to give Link access to the Remote Bomb, Magnesis, Stasis and Cryonis Runes. Accessing any one of these Guidance Stones and obtaining its rune will also allow Link to activate the amiibo Rune functionality which adds the amiibo Rune to the Sheikah Slate.
Within the Sheikah Towers, their purpose is to unveil each regional map of Hyrule with data on the Sheikah Slate. Once the Guidance Stone is used and the tower is activated, Link can warp back to the tower at a moment's notice. If Link can activate a second Tower, he will earn the Sheikah Sensor. Using a tower or shrine's Guidance Stone will activate and add its Travel Gate to the Sheikah Slate allowing Link to use them as warp points.
Within the Hateno Ancient Tech Lab, Purah happens to own a Guidance Stone herself. However, when Link first arrives to the Lab, it is shown that the Guidance Stone is inert as the blue fire that gives it power has gone out. Link must then search for the Ancient Furnace to acquire the blue flame using a torch, then must take the flame uphill while lighting the lanterns along the way to serve as a checkpoint in case his Torch goes out and finally, reignite the stove that fuels the Lab's Guidance Stone so that Link can obtain the Camera Rune, Hyrule Compendium, as well as restore photos taken by Zelda that that have a role in helping the restoration of Link's memories.
After taking a snapshot of Purah, she will then allow Link to upgrade two Runes and the Sheikah Sensor in exchange for some Ancient materials, these being three Ancient Cores for the Stasis Rune, three Ancient Shafts for the Remote Bombs, and finally three Ancient Screws to upgrade the Sheikah Sensor.
Purah and Robbie are shown to care for and dote on their Guidance Stones, becoming happy once Link restores power to them. All normal Guidance Stones are capable of rudimentary speech, though are generally depicted functioning more akin to a computer with a speech function.
If Link reads Purah's Diary, Purah will act as if she is angry about him reading it and pretends to use her Guidance Stone to erase all for the data and Runes stored on Link's Sheikah Slate, only to reveal it was a trick and that she had imitated her Guidance Stone's voice to make Link believe she had erased his Sheikah Slate's data (which Purah would not dare do anyways as Link needs the Sheikah Slate to regain his memories and complete his quest).
It is later revealed that the Sheikah Slate was designed to be used by the Hero Chosen by the Master Sword, thus explaining why Princess Zelda was unable to use the Sheikah Slate to access the Shrines, while the Towers remained buried under the ground. Princess Zelda and her Sheikah allies only realized this after the Great Calamity, thus explaining why Zelda did not have Link use the Sheikah Slate to activate them 100 years earlier. It is implied that had he been able to activate them with the Sheikah Slate, he would have been better prepared for the challenges he faced during the Great Calamity. It is strongly implied that the Guidance Stones, Sheikah Slate, Sheikah Towers, and Shrines where all created by the ancient Sheikah (which presumably includes the Sheikah Monks) to aid the hero in his quest to defeat Calamity Ganon when he eventually returned.
The Ancient Oven
In addition to normal Guidance Stones, during the Age of Burning Fields the Sheikah technology researcher Robbie modified his Guidance Stone at the Akkala Ancient Tech Lab to create the Ancient Oven Cherry which could convert guardian parts into ancient soldier gear. Later on, Robbie attempted to modify Cherry even further though his plans where too complex to implement and decided to put them on hold. However his wife Jerrin who had originally been sent by Impa to aid Robbie in his research, managed to complete Robbie's planned upgrades, allowing Cherry to speak like a living person. However Jerrin eventually became jealous of Robbie's interactions with Cherry as he came to rely on it more and more, which Robbie attributed to jealousy towards Cherry's namesake as he had named the Ancient Oven after his first love. After learning of his wife's feelings, Robbie chose to restore Cherry back to her original mechanical way of speaking and avoided referred to her as Cherry in order to avoid upsetting his wife, due to Jerrin's habit of throwing things whenever she heard her husband refer to the Ancient Oven as Cherry. Due in part to his old age, Robbie occasionally slip up and accidentally refer to the Ancient Oven as Cherry as shown when he reunites with Link one hundred years after the Great Calamity, though apparently Jerrin fails to hear him say it as it does not cause an outburst from her when he says it, though it is possible that Jerrin did hear her husband say it and simply keeps her emotions in check and lets it slide while in the presence of company as she may not wish to cause a scene in front of a guest like Link.
Eventually the blue flame Furnace that powered Cherry went out and Robbie was unable to relight it before Link's arrival as his old age prevented him from doing so and he couldn't ask his son Granté to do it as he had left to explore the world and Jerrin refused to relight it due to her dislike of Cherry. After proving his identity to Robbie, he is asked to relight the furnace that powers Cherry so she can make Link ancient soldier gear. Like with Purah's guidance stone, Link must relight the furnace with Blue Flame which he can obtain from the Ancient Furnace at Tumlea Heights in Deep Akkala. After restoring power to Cherry, Link can use her to forge ancient soldier gear in exchange for Rupees and Guardian Parts. Robbie requires Link to pay as due to Robbie lack of funding for his research as the Royal Family of Hyrule had originally funded both Robbie and Purah's research 100 years ago, funding which ended as a result of the Great Calamity thus Robbie compensates by using Cherry's ability to forge Ancient Soldier Gear as a means to generate revenue which he can use to fund his research.
Link can also relight the flame after receiving the 'Robbie's Research" Side Quest from Purah before he even enters the Akkala Ancient Tech Lab and speaking to Robbie. This will restore power to Cherry allowing Link to use her to forge Ancient Soldier Gear without speaking to Robbie or completing the side quest (as it is only completed once Link talks to Robbie after restoring power to Cherry). Additionally Robbie will not require Link to prove his identity if he speaks to Robbie after he relights the flame.