A library established and operated by a local government, open to the public. Often contrasted with 私立図書館 (private library) or 公開図書館 (library open to the public but not necessarily publicly funded).
See also: 公開図書館
I borrowed a book at the city public library.
Anyone can use a public library for free.
公開図書館 refers to any library open to the public, regardless of funding source, while 公立図書館 specifically means a publicly funded and operated library.
私立図書館 is a private library, often run by a private organization or individual, as opposed to a public one.
Compound of 公立 (こうりつ, 'publicly established') and 図書館 (としょかん, 'library').