Optional Memories will allow you to get 1+ specific Reward cards, a 100% Sync and a second chance to obtain a Chest that you missed before. You will also learn more about the past of your four Assassins.
You always get to choose: Either you play 1 Optional Memory when it is offered to you, or you ignore it for good (in this particular situation, continue the campaign by playing the next Memory).
When playing an Optional Memory, continue playing with all the cards and miniatures acquired or unlocked during the campaign (Equipment, Assassins, Events, Guards, etc.).