It wasn't a real club, in that there weren't meetings or officers or anything, like you might have in chess club or drama club. That's just what they called it.
It was funny, I grew up poor, but we always had money for books. Especially the Scholastic books, which were mostly paperbacks, back in the day. I'd always be the kid in class who got a big stack of them on book delivery day.
For my kids' schools, I would always buy the teacher's entire wish list at book fairs. I remember what it was like to be poor, books saved me, so I pay it forward. Book fairs had more hard cover books, and extras like posters, fancy pencils, etc.