The Library is a location, originally part of The Hotel, which has evolved into a location all on it's own.
The Library as a structure is almost impossible to fully describe. While originally a space constructed due to the unique features of The Hotel, the effects of the constant rebooting of the universe, as well as inhabitants attempts to delete it and restore it has transformed it into a unique time-space event. It simultaneously exists at the beginning and end of Earth 1337-A, while at the same time positioned outside of Time/Space itself. Due to this, the structure is trapped in a state of "timelessness," unaffected by the passing of years. It has been calculated to lay on a planet the size of Jupiter, though it more specifically exists not simply upon the surface this "world" but also within it.
The Library serves as the ultimate testament to The Hotel and it's inhabitants, containing within it the combined knowledge of every book ever published and to be published and entire wings dedicated to those who live, will live, or had lived in The Hotel.