noun
A library open to the general public, typically operated by a local government or public institution.
市の公開図書館で本を借りた。
I borrowed a book at the city public library.
図書館 is a general term for any library, while 公開図書館 specifically emphasizes that it is open to the public.
Compound of 公開 (こうかい, 'open to the public') and 図書館 (としょかん, 'library').