Why do I need this attribute?
I would guess that position is not really part of a relation, but rather an ordering key used to denote what book is the user's first, second, third and so on.

Or, like you say, it could be that a user can have multiple copies of a book, but that still wouldn't make position part of the relation, only of the primary key of UserBooks.

Or, a combination of the above two (ordering key and user can have multiple books).