What is an idyllic memory?

Answer 1

"Idyllic" basically means something like "extremely happy; peaceful".

It's also possible, if you heard the term rather than saw it, that the speaker was actually saying eidetic memory, which is more commonly referred to as a "photographic memory".

Answer 2

I believe you are referring to "eidetic " memory, a rare capability to have near-perfect recall. Many that claim to possess an eidetic memory do not have one.