This is an area that was actually much better on earlier cruises. It started out well stocked--mostly Hyperion publications (a Disney company) and books about Disney topics. There were a few board games, etc. There was a sign out book, and you could take items to your stateroom.
On later cruises, we found that the area tended to be locked quite a lot, and when we could get in the selection had diminished greatly--I suspect some users had items that went into their suitcases. On our most recent cruise, the library was locked both times I tried...
It is on deck 2 near the conference rooms/elevators.