Link has been sleeping for a century, and during this time, he has lost his memories of the past. "The Legend of Zelda: Breath of the Wild" story is about Link trying to save Hyrule and stop Calamity Ganon, but there is a subplot about getting his memories back.
Link has 18 memories to retrieve to understand what happened a century ago. Some are part of the main story, but many will need the players to do some detective work. (Warning: Spoilers ahead. If you don't want to learn about the story, please stop reading.)
Some memories are directly part of the main story and mission, and players do not need to find a specific location because these memories will be regained as part of the story. Some of these memories are Zora Domain, Gerudo Town, Rito Village, Goron City, and Master Sword.
When the player reaches Kakariko Village, he needs to find Purah of the Hateno Ancient Tech Lab who will teach the payer more about his Sheikah Slate. She will unveil the final Rune in his slate after completing a task for her. The final Rune is a camera which comes with different images of landscapes in Hyrule shot by Zelda a century ago. Purah believes that if Link finds these locations, his memories will return. These are locations the player needs to find. Pikango the painter from Kakariko Village in front of Impa's house can also tell the location of one picture. The player will see Pikango in horse stables across Hyrule and tell him the location where a ring of light will allow Link to recall a memory.
The first photo shows a knighting ceremony area south of Hyrule Castle while the second one shows Lake Kolomo. Photo number 3 is of the Ancient Columns across Tabantha Bridge where there is a cliff to the south. Atop the cliff are ruins outside Tena Ko'sah Shrine. The fourth image is of Kara Kara Bazaar by the pond whereas the fifth photo shows the west of Goronbi Lake in the Goron region. The player needs to look for the Woodland Stable or Mirro Shaz Shrine and proceed North.
In the sixth photo, the player has to look for the Serenne Stable and proceed southeast to Hyrule Castle. A body of water will be seen past Salari Hill. Photo number seven shows a location in West Necluda near Scout's Hill and northeast of Hylia bridge while photo number eight shows a location in Hyrule Castle. The ninth lost memory location is at Spring of Power in the Ruins of the North Akkala Valley between Ordoc Quarry and North Akkala Valley while the 10th is in Sanidin Park Ruins near Safula Hill. The 11th photo is on snowy mountain Mounth Lanaryu where a gate below Mount Lanaryu, west of Naydra Snowfield is found. Lastly, photo number 12 is at the Northeast of the Bottomless Swamp along the Hylia River. Note that the list is still being compiled.