Databases are the way to organise lists of data. Data is information in a raw unorganised form. If the data is a collection of small items then you can use a database to organise the data in the same way as you would use a filing cabinet to organise documents.
Some data does not fit in a database but you can use a database to index the data. If the data is a collection of art in a gallery, the database can store information about the art in an organised fashion. An index of digital image files could be placed in to a database so that you can select lists of images in all sorts of sequences.
Databases work best with lists of data. Some people push special databases designed for data in unstructured forms or in highly structured hierarchical forms. Internally those special databases work with lists of lists where the lists are very short and often occur at many locations. When you want fast access to a set of data in a non standard database, the database build a list of lists which is effectively a conventional database hidden within the non standard database.
The language of databases is SQL which stands for Structured Query Language. The structured part means that you can have queries within queries. When you build a query to find all the birds that nest in and around cities within Australia, you might start by writing a query to find all the cities in Australia. You can then write a query to find all birds that live in a specific city. You can then structure the query by placing the list of cities query within the list of birds query. The query finds all the cities in Australia and then finds all the birds nesting in those cities.
The are books on databases and SQL listed under Books, Database Books. The following articles talk about various databases and related technology.