Captured Memories

Captured memories is a quest given to you by Purah when she uploads Zelda's pictures to your Sheikah Slate. You are told to go visit Impa. When you visit Impa. She will tell you to go to the places where the pictures were taken. (She doesn't really tell you how which is annoying). When you get you first memory go to impa and she will give you the Champion's Tunic

Finding the memories
The way to find the memories is just to do side quest in till you found someone who knows where a picture is.

Fairy Fountain
One of the memories is Find the Fairy Fountain given to you by Pikango. You will find him just walking around in Kakariko Village. Once you do that quest he will tell you where to find one of the memories. If you forget where it is you can find him again ad he will tell you.) Its at Lanayru Road-east gate. Try to go to Nayara Snowfield from the fountain and you will find a path next to a river (or do what the game said but I found this easier). Follow that path up to a little glowing thing and it will say recall. Do that.