“Peek-a-boo” (the noun) is a term most commonly associated with the young children’s game of the same name, which dates back to the 1590s. The game is played by one person covering their face then opening their hands suddenly, revealing their face and saying “peek-a-boo.” There are several variations of the game, but you get the general picture; the point is the fun and whimsical element of surprise.
“Peek-a-boo” (the adjective) can also mean “see-through”. This use dates back to the late 1800s. It was a term commonly associated with sheer or eyelet fabrics.
Where did it come from?
I could find very little about the history of this term. I did run across a few mentions that the possible origins of the term “peek-a-boo” are derived from the French game of pique-a-beau. This really wasn’t as much of game as it done to indicate displeasure with one’s beau. A young lady would cover her face briefly to display her displeasure. I couldn’t verify this, however.