What is a "database"?

There was lot of discussion in this question: https://dba.stackexchange.com/questions/18669/what-database-technologies-do-big-search-engines-use So much discussion that it made me confused. So... what is a database, anyway? Are only relational databases "databases"? Are object-oriented databases "databases"? Is any system that allows me to store and retrieve information (like a map, list, etc) a database? Or does a database have to store/retrieve information and also have some administration features like Users and Privileges? Was dBase III plus a database, since it wasn't really relational?