A large part of the story in The Legend of Zelda: Breath of the Wild is tied to Captured Memories, optional side quests that help fill out the game's backstory.
All Memory Locations in Breath of the Wild – Captured Memories | Austin John plays
There are 18 memories to collect: 13 are linked to photos from the Captured Memories Quest, while the remaining five appear as you complete the main story.
To begin the Captured Memories Quest, you must first speak to Purah in Hateno Village. Purah is tied to the Locked Mementos Quest, which you will receive from Impa after speaking to her in Kakariko Village.
After you find Purah (you can find her in the Hateno Ancient Tech Lab north of Hateno Village) and complete a task for her, she will repair your Sheikah Slate. You will then need to return to Impa, who will task you with finding Princess Zelda's lost memories, which are tied to photographs she took with the Sheikah Slate.