Databases are searchable collections of data or information - Google is one kind of database. In the academic world databases focus on particular types of information (journal articles, books etc.). Academic databases also tend to specialize on a particular subject area. ATLA is the key database for Theology and therefore focuses quite narrowly on this area - if you are interested in exploring topics more broadly it will be worth considering other databases.
The amount of full-text available will vary from index to index. Often a Connect button will be available and this will either link through to full-text or enable you to search QCat for the book or article. Please note that the Connect button does not guarantee that full-text is available.