The “On This Day” feature works with both content you posted, status updates, photos, posts from friends and other things you have shared, and content you were tagged in.
This new feature came up because Facebook thinks "people often look back at old photos and other memories they’ve shared on Facebook, and many have told us that they enjoy products and features that make this easier."
Naturally, only you can see your "On This Day" posts but you can elect to share some of these moments with your friends.
Your "On This Day" page can be accessed any time via the "On This Day" bookmark, searching for “On This Day” or visiting facebook.com/onthisday.
The new feature is still in the testing phase and will roll out gradually to all Facebook users on the web and mobile.