Why does my baby love playing peek-a-boo?

Peek-a-boo... ...Plays into a new skill children acquire at 6-9 months of age: object permanence -- they can still hold an object in their mind when it becomes invisible. It tickles them pink that this also applies to people, and peek-a-boo reassures them that, if you come back after a short departure (when their eyes are closed), you will also come back after a longer one.
It is exciting! Your baby loves peek-a-boo for the interaction as well as the surprise they experience when you "disappear" and then "reappear" out of thin air! even after they sense object permanence (objects still exist even when they are out of sight) at about 8-12 months this game still remains fun.