The Library on HEXRPG is a place for user-submitted books to be available for free. There is no particular incentive for posting books, although it is a useful place to store information and many clubs that include interactive lessons use Library books to get lessons up.
It includes a search feature both for author and title, and is usually used for lessons or textbooks.
While there is fanfiction that can be found (indeed, there is a section for just that) there is also a fanfiction section on HEX that can be accessed and is better in most ways for finding fanfiction.
The main benefit of the Library is the cost - there isn't one! There are no loans out, unlike a real library, but there is no need to purchase the books either.