It is not known where the Black Library is, only that it is a "dark Craftworld". We also know it was very far away from the center of the Eldar Empire, when she who thirsts was born. Harlequins have a greater understanding of the Warp and its effects than any other Eldar, so the Black Library could potentially be in the Warp, in the real world, or somewhere in between.
The Black Library has been described a a massive complex, where the Eldar gather all of the information on the Chaos gods and their servants, possibly to find a way to destroy them. Very few Eldar have ever seen the inside of the library, and even fewer non eldar have entered.
In the Thirteenth Black Crusade of Abaddon, Ahriman of the Thousand Sons was able to penetrate the webway into the Black Library, attempting to gain the important documents hidden within. However, a guard of Harlequins and Eldar warriors were able to drive the Chaos Sorcerer back.