A database is a collection of material within a limited subject. Usually a database consists of materials such as articles in full text or as abstracts and books but a database can also include images or videos and much more.
Bibliographical databases collects information about articles, books, reports and other published material in a specific subject. It can be a geographical area, a time period or a research area. Usually you don't get access to the fulltext in the database, so you have to find the fulltext via other search systems.