In Final Fantasy V, the Ancient Library is a location you must visit several times during the progress of the game for various reasons. The first time you visit, fairly early into the game, is to find Mid, the grandson of this game's Cid. who is reading a book deep in the basement, unaware of your party fighting through monsterss to reach him. At this point, you also pick up the esper Ifrit.
Later on in the game, near the end, it is neccesary to visit the library again to read a lost book, which, with the interpretation of the Turtle Sage Ghido, is needed to progress in the game.
That being said, the main reason that the Ancient Library fits in so well with Final Fantasy is because it gives a glimpse of ancient secrets stacked up in thousands of books. Final Fantasy, like all good fantasy, succeeds because it gives a glimpse of a larger story without explaining what exactly that story is. And this library, filled with scholars nervously looking over tomes, communicates that well. It's a shame you can't look in any of those books.
Strangely enough for a library, the music in this section is rather fast paced and urgent for a library. However, it is a library filled with rather angry, violent monsters.