Link's memories will be recovered by visiting the statues of Hylia. Each memory will be of an instance in which Zelda/Link went around Hyrule planting these flowers (perhaps 1 in each region? 18 memories, 16 known regions + the castle).
The math works better if I take into account that we can see three flowers in front of the Deku Tree. 3 flowers here in this region, and 15 flowers for the other 15 regions (including the Great Plateau). These three would be planted by Zelda when lodging the Master Sword in front of the tree after Link's presumed demise.
I imagine that at some point soon after departing the Plateau (presumably with some preliminary guidance given by Daphnes), the Main Story will split into two overarching but intertwining Quests.
One to learn about and tackle the Guardians (both giant and normal)
One to go around collecting memories -> collecting flowers
Completing both would put the player (and the world) in the ideal position to tackle Ganon at the end of the game.
The actual significance of the flowers I am still unable to determine. However, it
may to be something that reconciles the fact that Zelda (and Link) found the need to do so 100 years ago. This would imply at least one of the following:
A.) The flowers were being put into place in order to deal with some immediate threat/issue
B.) The flowers were put into place as a precaution for a potential future threat/issue
Alternatively, Zelda was unable to complete this quest in the past and Link now sets off to finish planting the remaining flowers in order to
bring about whatever effect they were meant to have.