It is most prominently featured in the animated series.
The library has two floors, both of them filled with dozens of cabinets with books about every conceivable subject. In the center, there is a large open section with a ceiling window.
On the second floor is a hidden entrance behind a bookcase, that leads to a secret room filled with spell books. Hilda discovered this room in "Chapter 8: The Tide Mice". In "Chapter 3: The Witch", this secret room turned out to be the first in a series of secret rooms and passages that eventually lead to Witches Tower.
The library is supervised by The Librarian.
The library is also briefly seen in the graphic novel "Hilda and the Black Hound", but it looks notably different there than in the animated series. In "Hilda and the Stone Forest", one panel shows Hilda and Frida in the library, summoning a spirit from a book. This implies the Library in the graphic novels also has the secret room with magic books.