Technically, a "database" is just an organized collection of data. While nowadays it's increasingly rare to encounter a non-electronic database, these were once upon very commonplace. One specific example that I recall rather fondly is the list of Dewey Decimal cards that libraries would keep in narrow file cabinets so that users could search through them and find the books they wanted. While my school library's catalog was already digitized, I still used these cards sometimes, finding books that had been omitted from the digital system for whatever reason (though these were eventually cleaned up when the digital system itself started to include the creation of spine labels, thus causing non-cataloged books to become more obvious).